Captain Fabregas and his team mates were in a different class to Boro as they closed the gap on third-placed Chelsea to six points with four games remaining.
Arsenal are 12 points behind leaders Manchester United and although the title has long been out of reach the Gunners are now virtually assured a top-four finish and Champions League football next season.
"We want to catch Chelsea and we will give absolutely everything in the last four games," Arsenal manager Arsene Wenger said. "We play Chelsea at home so you never know.
"Victory was important for us before we go to the semi-finals of Champions League against Manchester United."
Boro's 10th consecutive away defeat in the league left them third from bottom, three points behind Hull City who are just above the drop zone.
Blackburn Rovers, another team scrapping near the bottom of the table, edged towards safety with a 2-0 home victory over mid-table Wigan Athletic.
Striker Benni McCarthy and defender Ryan Nelsen scored to lift Rovers six points above the relegation zone.
Arsenal, who face United in the first leg of their Champions League semi-final at Old Trafford on Wednesday, had only two moments of concern.
NEARLY EQUALISED
Former Gunners striker Jeremie Aliadiere nearly equalised and experienced defender Mikael Silvestre was substituted at halftime with a knock.
Aliadiere went through on goal in Boro's best chance but his shot was saved by the heel of goalkeeper Manuel Almunia.
Arsenal led from the 26th minute when Fabregas released Andrei Arshavin and swept in the Russian's cut back from inside the penalty area, although Boro complained that Nicklas Bendtner was offside.
"Bendtner is clearly interfering with play because he is stood in front of the goalkeeper," Boro manager Gareth Southgate told Sky Sports. "That hasn't gone for us but maybe we will get one at home next week against Manchester United.
"All the games are crucial for us now. While there is hope we have to keep fighting and we will.
Boro showed more urgency after the break but were killed off after 67 minutes when Fabregas took the ball around out-rushing goalkeeper Brad Jones and slid his shot into an empty net.
Manchester United lead the table from Liverpool by three points with an extra game to play after coming from two goals behind to beat Tottenham Hotspur 5-2 on Saturday.
NEWS: Silvestre doubtful for United showdown
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