City were left chasing shadows from the fifth minute at Eastlands after defender Dedryck Boyata saw red for a last-man foul on Marouane Chamakh and Arsenal won with goals by Samir Nasri, Alex Song and Nicklas Bendtner.
Chelsea, who beat Wolverhampton Wanderers 2-0 on Saturday, lead the Premier League standings with 22 points.
Arsenal and City are both now on 17 points, alongside Manchester United after Hernandez struck four minutes from time to seal his side's first away league win of the season.
In Sunday's other match, Liverpool claimed only their second win of the season when they beat Blackburn Rovers 2-1 at Anfield, with Fernando Torres among the scorers.
Arsenal had Cesc Fabregas back pulling the strings in a league game for the first time in five weeks and he made a huge difference with a display full of promptings and probings.
Before five minutes the hosts were up the hosts were reduced to 10 men when Fabregas slid a perfect pass into the path of Chamakh and Boyata dived in needlessly to bring him down just outside the box.
Arsenal soon made their numbers pay when Nasri played a nice one-two with Andrei Arshavin before scoring from a tight angle in the 21st minute.
Fabianski was called into action to foil Silva again as City started the second half brightly but the fluttering flame was extinguished when another Fabregas pass caused chaos and allowed Song to poke in the killer second goal after 66 minutes.
Bendtner came off the bench for his second appearance of the season to complete the scoring two minutes from time.
After Rooney had hogged the headlines all week it was his stand-in Hernandez who was the toast of Manchester United fans after his double overcame battling Stoke.
He opened the scoring with a dextrous back-header after 27 minutes but as United eventually sat back to defend their lead, Stoke substitute Tuncay Sanli curled in a lovely equaliser after 81 minutes. Mexico striker Hernandez, however, topped an impressive all-round display by seizing on a loose ball to prod in the winner four minutes from time.
Liverpool remain in the bottom three on nine points but there was a real feeling of relief around Anfield as they not only chalked up a rare win. Sotirios Kyrgiakos put them ahead early in the second half with a header and after a Jamie Carragher own goal in the 52nd minute, Fernando Torres grabbed the winner a minute later with only his second goal of the season.
