The Spanish captain got his name on the score sheet on 26 minutes, receiving the ball from Andrey Arshavin before pushing it past keeper Jones for 1-0. Middlesbrough called for off-side but had their claim denied.
The second goal came seven minutes after the hour as Fabregas rounded the goalkeeper to double the advantage.
As was expected, Arsenal were clearly the stronger side and the victory was fully deserved.
LONDON (AFP) - Cesc Fabregas admitted he'd forgotten what scoring a goal felt like after twice finding the net in Arsenal's 2-0 win over Middlesbrough in the Premier League at the Emirates Stadium here on Sunday.
The Spain midfielder was on target either side of half-time as the midfielder scored his first goals since October to help boost Arsenal's morale ahead of Wednesday's Champions League semi-final first leg against English and European champions Manchester United at Old Trafford.
"It's been a long time" Fabregas told Sky Sports.
"I had completely lost the feeling of scoring a goal. To score two in a game is always special but the feeling was amazing.
"It keeps going the run we have got in the league and three days before the Manchester United game, which is probably our most important one of the season, it's good for the confidence.
"We played some good stuff, we moved the ball really quick, and every player was good so we are happy with that."
Looking ahead to the United match, Fabregas added: "The defence will be really, really important. We know they are a great team, we respect them a lot and we love the way they play.
"I think they respect us well and it will be a good game, I'm sure."
While victory kept Arsenal's hopes of securing automatic qualification for next season's Champions League alive, defeat left Middlesbrough in the relegation zone and three points adrift of safety.
Boro's next match is at home to United on Saturday - a match sandwiched by the two legs of Alex Ferguson's side clash with Arsenal - but manager Gareth Southgate did his best to remain upbeat after the north-east team's 17th league defeat of the season.
"It's about what we do from here on in now," he said. "We've got a massive game at home next week and we've got our fans behind us there and it's a more realistic chance of getting something," the ex-England central defender added.
"I don't think it really matters when you play teams, it's about how we are on the day," Southgate said when asked if United's European commitments might work in Boro's favour.
"We will have to play extremely well. But we are capable, we've done it in the past.
"We've said we've got to pick some big results up, results went for us yesterday (Saturday) so we are still in with a chance but we realise we've got it all to do."
LONDON (AFP) - The sight of Arsenal stretching every sinew in this week's thrilling 4-4 draw at Liverpool will have done nothing to lift the mood of Middlesbrough manager Gareth Southgate.
Desperate for points to boost his Middlesbrough side's increasingly desperate survival battle, Southgate will have hoped Arsenal's thoughts were now firmly fixed on next week's Champions League semi-final first leg with Manchester United.
But the evidence at Anfield suggested that Arsene Wenger's team have no intention of relinquishing their 19-game unbeaten league run - even though their title hopes have gone and a top-four finish is now all but guaranteed.
That sends out an ominous message to Boro who visit the Emirates Stadium on Sunday, three points adrift of safety and just one defeat away from equalling the club record of ten successive league defeats away from home.
Wenger believes his young side is maturing fast and is unrecognisable from the side that struggled during the opening months of the season.
The fact that this is the club's longest unbeaten league run since the so-called 'invincibles' lifted the title in 2004 without suffering a single defeat would appear to back up the manager's claim.
The decision of the FA to charge Cesc Fabregas for the alleged spitting incident that followed Arsenal's FA Cup victory over Hull City has cast a rare shadow over the club's upbeat end to the campaign.
But while Wenger insists his captain is innocent, his concern about any possible suspension is tempered by the fact that it will be limited to domestic games only - and not hinder the Frenchman's bid to guide his side to the success in the one competition that has eluded him during his 13-year reign.
The other area of concern for example is the form of his defence whose performance against Liverpool will have given Boro at least some hope.
Wenger's analysis of that game suggests he will make changes in that department with one eye on Old Trafford next week.
"I believe that our defenders are the only players who played Wednesday night against Villarreal, Saturday against Chelsea, Tuesday against Liverpool and so at the end of the game, we were a bit jaded physically," admitted the manager.
Robin Van Persie will also miss out with a groin injury that will almost certainly keep him out against United.
But Andrei Arshavin, the four-goal hero at Anfield, will definitely play on Sunday as he is cup-tied for European competition.
Wenger may also be tempted to bring back Togo striker Emmanuel Adebayor.
"Adebayor should come back into training on Saturday and he could be in the squad. But Van Persie is definitely out," said Wenger.
Four points from the last two games have rekindled Boro's hopes of avoiding relegation but Southgate can at least draw confidence from his record of never having lost to the Gunners in five games since he took charge of the North East club.
"We want to go there and win," Southgate said. "Time's running short for us.
"Teams have been there and won there this season so we've got to take heart from that and the Emirates Stadium has been a happier hunting ground for us than Highbury was.
"We know we're going to have to produce some big results between now and the end of the season - and we might as well get on with it this weekend.
"They're 19 league games unbeaten and they'll want to continue that. But their biggest game of the season is Wednesday night (against United) and there has to be an element of that in the background for them."