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Arsene Wenger's side trail leaders Chelsea by six points and are now just two points behind second-placed Manchester United after the champions lost at Everton.
The Gunners looked to be out of the reckoning after their defeat at Chelsea earlier this month, but United and Chelsea have both slipped up at Goodison Park to put the north London club back in the hunt.
After their error-strewn 2-1 midweek defeat at the Porto in the Champions League, Arsenal captain Fabregas was openly critical of the way his side conceded their goals, with goalkeeper Lukasz Fabianski particularly guilty.
As a result, Polish international Fabianski lost his place in the starting line-up with Manuel Almunia recovering from his finger injury in time to feature.
Alex Song also returned to the starting eleven, while injured duo Andrey Arshavin and William Gallas remained sidelined.
Arsenal's problems in Portugal should be less damaging in the long term compared to Sunderland's worrying slide towards the relegation zone.
Steve Bruce's team have not won in the Premier League since November -their last three points ironically coming against Arsenal at the Stadium of Light thanks to a 1-0 win.
Bruce was boosted with the news that Kieran Richardson, Anton Ferdinand and John Mensah recovered from their respective injuries.
But it was Mensah's defensive partner George McCartney who was tested first as Fabregas played in Theo Walcott. The winger beat McCartney for pace but pulled his shot wide.
The home side dominated the opening 20 minutes with Samir Nasri seeing his shot deflected narrowly wide.
Walcott again left McCartney trailing in his wake only to see his shot blocked by Craig Gordon before Bendtner fired wide.
Bendtner came even closer to opening the scoring in the 17th minute when his effort deflected off McCartney and looped onto the crossbar.
The Denmark striker was celebrating his first goal since October 28 as he made it 1-0 in the 27th minute.
Emmanuel Eboue made a strong run into the box and his scuffed shot found its way through to Bendtner at the far post, who tapped into an empty net.
Kenwyne Jones had a great chance to level for Sunderland five minutes before the break but fired wide with only Almunia to beat.
Arsenal started the second half with a flourish and could have been 2-0 up inside the opening three minutes. Thomas Vermaelen was fractionally away from connecting with a Fabregas free-kick.
Walcott then showed a good turn of pace before producing a low shot which drew a fine save from Gordon.
Arsenal continued to apply the pressure yet for all their industry in midfield they were lacking a clinical finisher up front, as Fabregas, Bendtner and Walcott wasted chances.
Sunderland meanwhile saw a rare opportunity go begging when Darren Bent planted his shot straight at Almunia.
Referee Steve Bennett awarded Arsenal a penalty in the 90th minute when Fabregas was fouled by Fraizer Campbell.
Fabregas kept his composure to side foot past Gordon with virtually the last kick of the game.
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