The Gunners moved to within one point of fourth placed Tottenham with only one match remaining.
And it promises to be a nerve-jangling afternoon on Sunday with Arsenal at home to Wigan while Spurs travel to London neighbours West Ham.
Arsenal, playing their third game in six days, took the lead after half an hour and Fredrik Ljungberg could not have chosen a more timely moment to score his first goal of the season.
City were soon on level terms through a goal from defender David Sommeil, but Arsenal's class told late on when substitute Jose Antonio Reyes struck twice.
And there was also cheer for England coach Sven Goran Eriksson who was at Eastlands and witnessed Ashley Cole's first start for seven months and Sol Campbell continue to make excellent progress following his lengthy absence.
But it was another black night for City who, despite their impressive showing in parts, slumped to their eighth defeat in their last nine Premiership matches and a club record fifth successive home loss.
The Gunners, despite their gruelling run of games, fielded a strong side although Cesc Fabregas, Robert Pires and Reyes were all on the bench.
Arsenal made the breakthrough after half an hour when Thierry Henry made a run from the centre circle and released Ljungberg who breezed past defender Micah Richards to score with a low shot.
There was an element of fortune, however, as television replays revealed that Ljungberg was marginally offside before receiving the ball.
City were on level terms within eight minutes following dreadful defending from Arsenal as Trevor Sinclair's free header from Joey Barton's corner was fumbled by keeper Jens Lehmann enabling Sommeil to stab the ball home from a couple of yards.
The equaliser stung Arsenal into action and in the dying minutes of the opening period Campbell and Henry both went close to regaining the lead for the Gunners.
And the second half saw Arsenal continue where they had left off as Robin van Persie forced keeper David James to make a super save while Ljungberg's drive struck the upright.
Arsenal maintained their stranglehold as James denied van Persie and Aleksandr Hleb, but they were unable to find a way to goal.
And against the run of play City almost snatched the lead twice in as many minutes.
Lehmann came to their rescue making spectacular saves to keep out headers from Richard Dunne and Richards.
City also felt aggrieved not to be awarded a penalty following a challenge by Kolo Toure on Darius Vassell after he burst into the penalty area.
It was a measure of Arsenal's desperation to win that by the 72nd minute they had brought on Reyes, Fabregas and Pires.
And the changes reaped almost immediate reward when Reyes scored Arsenal's second within six minutes of making his entrance.
Pires released Emmanuel Eboue on the right and he cut the ball back for Reyes whose low shot squirmed under the body of James.
Arsenal sealed victory in the 84th minute when Henry set up Reyes who scored his second goal with a delightful effort which was curled into the top corner of the net.