The champions were looking to bounce back from their shock defeat at Newcastle in the week and needed just 48 seconds for the Argentine to open the scoring.
Alex Iwobi's howler proved costly when he tried to take it round Aymeric Laporte deep inside his own half.
The left-back robbed him of the ball, whipped in a pinpoint cross and Aguero was left with a close range header to beat Bernd Leno.
Arsenal could have easily crumbled and Laporte thought he had instantly doubled their advantage from a free-kick but his header was narrowly ruled offside.
But threatening to tear up the script, the Gunners found themselves level on ten minutes when Laurent Koscielny was left unmarked to head home Lucas Torreira's corner.
Unai Emery's side continued to grow in confidence with Pierre-Emerick Aubameyang and Torreira squandering half chances.
However all their good work was undone minutes before half-time when Aguero tapped home Raheem Sterling's cross.
City came straight out of the blocks in the second period and were determined to kill the game sooner rather than later.
And bang on the hour mark the game looked out of sight for the visitors when Aguero slid home Sterling's drilled cross, albeit controversially.
Arsenal players were incensed that the ball hit Aguero's arm on its way into the goal but their appeals fell on deaf ears.
It was his 14th Premier League goal of the campaign, sixth in his last four and number 219 for the club.
Emery responded by introducing ex-Man City academy prospect Denis Suarez for his Arsenal debut and the departing Aaron Ramsey.
But the Gunners looked shattered from their first half exploits with Pep Guardiola's unlucky not to add to the scoreline.
They will now be cheering on West Ham against Liverpool on Monday night after moving two points behind Jurgen Klopp's side.
Arsenal drop to sixth in the table, three points behind fourth-placed Chelsea.
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