The Gunners have cut the back on their rivals to thanks to goals from Alexis Sanchez and Mesut Ozil.
Arsene Wenger’s side have retaken 6th ahead of Everton and are now seven points behind 4th placed Manchester City.
A superb Alexis Sanchez free-kick opened the scoring three minutes before the break.
But Arsenal were pegged back five minutes after the restart when Stewart Downing cut in from the right to cross for Alberto Negredo. The striker prodded the ball home for his 8th league goal of the season.
The Gunners retook the lead 20 minutes from time after a silky chest pass from Aaron Ramsey found Mesut Ozil, who cooly slotted the ball pass Brad Guzan and give Arsenal the much needed three points.
Arsene Wenger who switched his side to three at the back acknowledged the performance was far from perfect, but was pleased his team got over the line.
“We responded well. I think it was not perfect but the commitment and focus was there. At 1-1 we found a response and managed to win,” said the Frenchman.
“It [the top four] is mathematically still alive. We knew we needed to win. Now we have a little break with the FA Cup and then we come back again to the league.”