Fabregas, who had been out for more than three months, was majestic in the middle of the park, his passing and vision proving too much for City.
The visitors, though, were not without their moments, Robinho and Shaun Wright-Phillips showing flashes of play as bright as the glorious spring sunshine.
But City's backline was their downfall - and their disorganisation led to Arsenal's opener.
Fabregas floated in a free-kick from the right and a completely unmarked Adebayor thumped in a downward header in his first match for the club since early February.
Arsenal going from 'strength to strength' - Wenger
It was down the right flank that Arsenal were to enjoy most of their success, and City were not helped by the loss of Wayne Bridge after only 17 minutes.
However, it was Bridge's replacement, Fernandes, who almost restored parity for his side.
Wright-Phillips slipped in a brilliant pass for the Swiss midfielder but his shot struck the outside of the post.
Micah Richards had earlier seen a low shot saved after also being played in by Wright-Phillips, and those chances were warnings for Arsenal that they needed to be careful at the back as they pushed for a second goal.
But the home side came forward with such menace that it appeared inevitable City would concede again.
It took a fine save from Given to deny Toure at close range after the defender had cut in from the right.
And the City keeper produced another excellent stop from Arshavin, who had earned the space by playing a devastating one-two with Alex Song.
When the second goal did come it was again made by Fabregas, whose lofted pass was superbly weighted and left Adebayor the relatively easy task of rounding Given and slotting into an empty net.
Man City lacked energy - Hughes
Shortly after, Arsenal had a chance for a third goal, again with Fabregas the provider - this time the Spaniard swung in a corner that was headed narrowly over by Song.
When Fabregas was replaced by Aaron Ramsey on 79 minutes, the skipper left the pitch to a standing ovation.
By then City's attacking threat had almost completely disappeared.
Robinho had already been substituted, after he had faded badly, and Craig Bellamy cut a lonely figure up front.
Arsenal should have scored more but substitute Emmanuel Eboue blazed high and wide and Walcott tested Given a couple of times.
But it was a comfortable victory for Arsenal, and revenge for the 3-0 reverse suffered at Eastlands in November - their last defeat in the Premier League, 17 games ago.
Arsenal manager Arsene Wenger:
"Adebayor got on the end of both goals for us but overall it was a very good team performance.
"I am delighted that we have come back strongly after the international break. We go from strength to strength from game to game, and that's very good to see.
"We are motivated. The players are hungry and up for it, and we have quality in the team."
Manchester City boss Mark Hughes:
"It is difficult to take any positives out of the game. We were well beaten.
"We had things to contend with. We lost Wayne Bridge and Vincent Kompany and that affected our gameplan.
"Really, we just didn't have enough energy on the field. Our passing was also poor and we played into Arsenal's hands in the end."
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