Germany were given a major scare before beating Algeria 2-1 on Monday to book a FIFA World Cup quarter-final meeting with France.
After a pulsating 90 minutes in Porto Alegre had ended goalless, Chelsea forward Andre Schurrle - on as a half-time substitute for Mario Gotze - cleverly flicked in Thomas Muller's low cross two minutes into extra-time to give Germany the lead.
Mesut Ozil added a second late on to wrap up victory for Joachim Low's side, before Algeria, who performed admirably throughout, gained a consolation through Abdelmoumene Djabou.
The result meant Algeria were unable to exact revenge for the "Disgrace of Gijon", when West Germany and Austria played out a mutually beneficial 1-0 scoreline that saw both sides through from the group at the expense of Algeria in the 1982 finals in Spain.
With many pointing to that infamous match as motivation for Vahid Halilhodzic's men in the build-up, Algeria flew out of the blocks in the opening 20 minutes, cutting through the German backline on a number of occasions and seeing an Islam Slimani goal disallowed for offside.
The African nation - making their first appearance in the second round - continued to impress, but Germany, who will now face France at the Maracana on Friday, finished the stronger and remain on course to reach the semi-finals of a fourth successive World Cup.
Algeria made a flying start and Manuel Neuer had to make a sliding tackle to deny Slimani an effort on goal from wide on the left in the ninth minute, after the goalkeeper had initially misjudged a charge from his line.
Sofiane Feghouli wasted a good position six minutes later, blazing the ball wildly across goal from the byline with two team-mates better placed.
Slimani converted Faouzi Ghoulam's wonderful cross from the left with a diving header in the 17th minute, but the referee's assistant correctly ruled that the Sporting Lisbon man had strayed offside, before Ghoulam flashed another effort narrowly off target as Algeria continued to dominate.
Germany gradually grew into the game towards the end of the first half, Muller heading wide and Ozil testing Rais M'Bolhi with a dipping effort.
Yet Algeria hit back in the 39th minute, Mehdi Mostefa thumping in a shot from 25 yards which deflected off Jerome Boateng and past the left-hand post with Neuer completely wrong-footed.
M'Bolhi made a superb double stop two minutes later, parrying Toni Kroos' drive away and then springing to his feet to keep out Gotze's rebound.
Germany enjoyed a more assured opening to the second period, Schurrle seeing an effort deflected just wide before Skhodran Mustafi, who replaced Mats Hummels (flu) in defence with Boateng switching to centre-back, headed straight at M'Bolhi from Kroos' delivery.
Philipp Lahm went close in the 55th minute, his curling effort diverted wide by an acrobatic save from M'Bolhi.
As the game wore on the play became stretched and Slimani sent a rasping effort from distance straight into the arms of Neuer 15 minutes from time.
Germany responded strongly and Muller ought to have scored his fifth goal of the tournament shortly afterwards, but his powerful header was beaten away by M'Bolhi.
Muller had another clear chance moments later, stabbing the ball wide after a glorious touch to bring the ball under control, while Bastian Schweinsteiger was unable to seriously trouble M'Bolhi with a weak header from Lahm's chipped pass.
Low's side then struck early in the first extra period, Schurrle adjusting brilliantly to backheel Muller's cross from the left into the net.
Algeria could have levelled through Mostefa, who snatched an effort wide from 10 yards after Germany failed to deal with a corner.
Ozil then made the game safe in the closing stages, lashing high into the net after Schurrle had been denied just in front of the goalline by Essaid Belkalem, although there was one final twist as Djabou converted a right-wing cross at the back post to net a deserved consolation for Algeria.
|Coach: J. Löw|
for M. Götze 46'
for S. Mustafi 70'
for B. Schweinsteiger 109'
|Brannagan open to Championship loan move|
|Wenger wants to sign Mertesacker replacement|
|Ancelotti: Bayern´s transfer business done|
|Brisbane Roar sign former Danish international Kristensen|
|Verratti, Luiz missing for PSG|
|Sounders part ways with foundation coach Schmid|
|Mane turned down Manchester United for Liverpool|
|Zidane on Pogba: Until August 31, anything can happen|
|Mkhitaryan driven by father´s death|
|Inter rejected Napoli offer for Icardi, says president|
|Clichy: City fighting fit after Guardiola pizza ban|
|Everton and Burnley win as Hull are held|
|Ajax held by PAOK after Cillessen howler|
|Conte left frustrated by ´crazy´ money in transfer market|
|Neymar makes Barcelona case to Gabriel Jesus|
|Rostov comeback twice for Champions League draw with Anderlecht.|
|Arsenal defender Mertesacker set for lengthy lay-off|
|Conte not selling ´fantastic´ Matic|
|Ibrahimovic keen on MLS and Beckham´s Miami project|
|Neymar: I play for Messi, he´s the man|
|Barcelona reveal details of Andre Gomes deal|
|Suarez bullish over Barcelona prospects|
|Ajax claim Napoli keen on Milik to replace Higuain|
|Totti labels Higuain´s Juventus move ´a disaster´|
|Juventus confirm Higuain deal|
|Pato to Villarreal ´in the final stage´|
|PSG sign Lo Celso|
|Muller: Beating Dortmund will be more fun this season|
|Juventus sign Higuain from Napoli for €90m|
|Pastore: I´m like God in Paris|
|Injured Lanzini out of Olympics|
|Allegri unperturbed by Higuain fee|
|Menezes replaces Bento at Cruzeiro|
|Sporting rejected major bids from Inter and Liverpool for Joao Mario, claims father|
|Pochettino pleased by Tottenham despite Juventus defeat|
|Eriksson: Allardyce the right man for England|
|Mourinho makes United train after stepping off plane from China|
|Hazard can still match Messi, says Pedro|
|Pjanic shows there is life at Juve, with or without Pogba|
|Juventus 2 Tottenham 1: Benatia bags win for Serie A champions|
|Dembele: I am not the Bundesliga´s next superstar|
|Lyon claim €35m Arsenal offer for Lacazette rejected|
|Donnarumma dreaming of Milan captaincy as he eyes long-term stay|
|Robson: Ibrahimovic can match Van Persie´s first year at United|
|Rooney should remain England captain - Eriksson|
|Emery wants new striker at PSG|
|Santos accept Juventus bid for Gabriel|
|Eriksson expects Sweden to try and tempt Ibrahimovic out of retirement|
|Spurs signing Janssen almost quit|
|Leicester stay best for Mahrez - Ranieri|
|Allardyce to take Mourinho cue on Rooney|
|Ings ready to outdo big-money signings|
|Henderson optimistic over Liverpool campaign|
|Allardyce hardened to the challenge of England post|
|Barcelona announce record revenues for 2015-16|
|Moyes enjoys Sunderland win as Palace beat Colchester|
|Stoke complete Allen signing|
|Roma coach Spalletti warns suitors off Manolas|
|Cresswell out for up to four months with knee injury|
|Burnley fan banned by club for racist abuse|
|Dad won´t let me play at the Olympics - Larsson Sr pulls rank|
|Kostic joins Hamburg on five-year deal|
|Tevez: I´d turn down Chelsea and Napoli to stay at Boca|
|Mayoral inspired by Benzema for Wolfsburg stint|
|Allardyce straight into competitive action with England|
|Liverpool, Sevilla fined for Europa League final incidents|
|Barcelona seal Guillemenot signing as part of new Servette deal|
|Niersbach handed one-year ban over World Cup corruption|
|Chelsea and Everton ´still interested´ as Koulibaly eyes Napoli exit|
|´Still working hard´ - Balotelli trains with Liverpool kids|
|Winter breaks, long-ball football and the World Cup: Allardyce in his own words|
|Inter warn Napoli Icardi is not for sale|
|Zanetti wants Simeone back at Inter|
|Stoke snap up Sobhi|
|PSG tougher under Emery - Lucas Moura|
|Totti not ready for retirement - Pallotta|
|Confident Allardyce reveals plan for England success|
|Pochettino to discard three Tottenham players|
|Allardyce: Rooney must wait for captaincy decision|
|Aubameyang: I will only leave Dortmund for Real Madrid|
|Allegri silences questions on Pogba|
|Bruce stands by decision to quit Hull City|
|Pochettino: Not the right time for Argentina job|
|Inter yet to approach De Boer with Mancini exit rumoured|
|Ancelotti trusts me more than Guardiola - Ribery|
|Wijnaldum rejected Everton for Klopp|
|Pre-season Manchester derby cancelled|
|Coutinho excited by ´fast´ Liverpool recruits|
|Cristiano Ronaldo and Conor McGregor step into the ring together|
|Mancini coy on reports linking Icardi to Napoli|
|Nolito reveals why he chose Man City over Barcelona|
|Inter 1 Paris Saint-Germain 3: Icardi absence in defeat fuels Napoli talk|