Northampton Town bounced back from their opening-day loss to claim a 3-1 win over Newport County in League Two on Saturday.
Aidy Boothroyd's men, beaten play-off finalists last season, lost out to York City in their first game but proved too strong for a Newport side that had emerged victorious from a midweek League Cup tie against Championship Brighton.
Early goals from debutant Jacob Blyth and 28-year-old Roy O'Donovan were followed up by a Gary Deegan strike, ensuring Connor Washington's effort was only a consolation.
But Newport were not the only League Two newcomers to fall to defeat in their second game, as Bury and Hartlepool United also lost.
The two relegated teams were brushed aside by Oxford United and Southend United respectively.
Hartlepool lost 1-0 despite playing for more than half the game against 10 men following Barry Corr's dismissal, but Freddy Eastwood's fifth-minute strike proved enough to make it two wins from two for the visitors.
Bury, who like Hartlepool came down from League One last season, were beaten 2-1 at Oxford, with Johnny Mullins' goal proving the difference.
There were more positive results for Mansfield Town and Portsmouth, though, who managed to clinch draws in their tough encounters after losing their league openers last week.
Portsmouth held Accrington Stanley 2-2 in the day's early kick-off as Peter Murphy and David Connolly scored both goals for their respective teams.
And Mansfield earned a point from their goalless draw with Exeter City after goalkeeper Artur Krysiak pulled off two stunning saves in the second half to prevent Paul Cox's team taking their first three points back in the Football League.
Saturday's action saw strong wins for Chesterfield, Dagenham and Redbridge and Fleetwood, with all three pulling off 2-0 victories over their opponents.
With Fleetwood's two goals coming within the first 15 minutes from David Ball, Plymouth were unable to retaliate despite enjoying the bulk of the possession.
On the scoresheet for Chesterfield in their win over Cheltenham Town were new signings Gary Roberts and Eoin Doyle, while Rhys Murphy and Brian Woodall slotted home for Dagenham to punish York.
Elsewhere in the League, there were draws for Bristol Rovers and Morecambe, who faced Scunthorpe United and Torquay United, with the former remaining goalless while Ryan Williams and Karl Hawley claimed one apiece in the latter.
And the second week of the season also saw three points for Burton Albion, who beat Rochdale 1-0, and AFC Wimbledon, who saw off Wycombe by the same score.
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