Rooney opened the scoring after 36 minutes before two yellow cards in quick succession for Kyle Walker—the latter very harsh—saw him sent off just before the break.
Raheem Sterling equalised in the 83rd minute, and five minutes later Morgan Schneiderlin received a similarly undeserved second booking.
City dominated the early exchanges as they piled pressure on the visitors, but it was Dominic Calvert-Lewin who had the best of the chances as he twice fired wide on the counter.
Phil Jagielka had to come to Everton's rescue midway through the half, though, when Sergio Aguero latched on to a free ball from Nicolas Otamendi's rebound off Jordan Pickford. The defender was on hand to head clear the Argentinian striker's attempted lob off the line.
City came close again when David Silva crashed an effort off the post, but just as they were beginning to turn the screw, Rooney struck.
The forward ghosted into space in the penalty area in time to convert Calvert-Lewin's ball from the right, marking a significant milestone:
Things got worse for the hosts soon after when Walker was booked for a late challenge on Leighton Baines, and moments later he received another yellow card for backing into Calvert-Lewin.
James Robson of the Manchester Evening News believed the second card to be harsh on the full-back:
Despite the setback, City began the second half as strongly as they had the first, though that didn't translate to clear-cut chances.
Substitute Bernardo Silva miscued a volley into the ground and wide, while Sterling twice blazed over, the latter from a promising position after pouncing on Aguero's lay-off.
Pickford was called into action to deny Danilo, getting down to his right to superbly keep out the Brazilian, but the Sky Blues' pressure eventually told when Mason Holgate headed a clearance straight to Sterling in the penalty area, and the winger made amends for his earlier misses with a clinical volley.
Schneiderlin, who had been booked in the second minute, then won the ball cleanly from Aguero with minimal contact between the pair, but he nevertheless received a second yellow card for his troubles in the 88th minute.
Match of the Day host Gary Lineker and football writer Tom McDermott felt he was hard done by, though the former called for better decision-making on the midfielder's part:
The two sides remain unbeaten after two games this season. City have a good chance of extending that when they take on Bournemouth on Saturday, but Everton will be tested again when they face Chelsea on Sunday.