The young England defender towered above the Black Cats defence to break the deadlock from Elano's free-kick, with Robinho on hand to make sure the ball crossed the line.
The goal ended a difficult first hour of the match for the hosts at Eastlands who had seen their side frustrated against 10 men and Robinho miss a first-half penalty.
Steed Malbranque conceded the spot-kick with his reckless challenge on Richards, but Robinho's stuttering technique did not fool Martin Fulop and the goalkeeper kept his side in it right to the end.
All this after George McCartney had been sent off in the 15th minute when tugging back Shaun Wright-Phillips as the winger was trying to latch on to a through ball into the box.
Brave effortDespite their brave efforts, Sunderland fell short up front and plunged further into the relegation dogfight following their eighth successive Premier League defeat against City.
Valeri Bojinov made a pleasing contribution in an open encounter before the whole dynamic of the game was changed in a mad three-minute spell as the quarter of an hour mark was reached.
Wright-Phillips had definitely got in front of McCartney in the chase to reach Elano's through ball. There was little doubt either the England winger would have been clean through.
Of more debate, certainly as far as Sunderland were concerned was the strength of the contact that forced Wright-Phillips to pull up as Fulop came to collect.
Referee Steve Tanner felt it was enough to merit a foul. It took assistant Mo Matadar to confirm the need for a red card.
Although Bojinov curled the free-kick over, City were presented with an even better opportunity to exploit their extra man on their next attack when Steed Malbranque upended Micah Richards, who had burst forward on the overlap.
For a player of Robinho's class, confidence should not be a problem in such situations.
But his trademark shuffle as he strode up, put doubt only in his mind. The shot that followed was weak and Fulop, a conclusive winner of that mind-game battle, made the easiest of saves.
After such a frenzy of incident, the game took a bit of time to draw breath. Yet Sunderland were not content just to sit back and soak up pressure.
If Jones' admirable industry had been matched by a bit more precision from his team-mates, the Black Cats might have presented their hosts with a stern examination.
Instead, City carried most of the attacking threat even if, aside from Robinho's penalty, they created nothing better against 10 men than they had done when Wright-Phillips had ended a splendid one touch move by lobbing narrowly wide when Sunderland still had the full compliment on the field.
The onus was clearly on the hosts to attack and Richards decided it was time to take centre stage.
Good enough to become the youngest defender in England history and win 11 caps during Steve McClaren's ill-fated reign, Richards has lost his way over the past 18 months, so much so that thoughts of going to a World Cup under Fabio Capello seem pretty remote.
But the defender is still only 20 and now slotted back into the right-back position McClaren used to favour, the youngster roared forward with gusto, as if Sunderland were the team to take all his frustration out on.
SquanderedOpportunities created for Wright-Phillips and Elano were both squandered - the former woefully, the latter agonisingly as a delicate flick rolled wide - so it was just as well Richards had found the net himself, rising to guide Elano's free-kick over the line just before Robinho could prod home.
It was his first goal for two-and-a-half seasons and only the third of a career that was launched with an 'F-word reaction' to a last-minute FA Cup equaliser in only his fourth game at Aston Villa in February 2006.
Unfortunately for Richards, his day ended early as he limped off with what appeared to be a hamstring injury, which cast a cloud on an otherwise impressive day.
1st Half Goals
Shots on Target
Shots off Target