City recalled Elano in place of Stephen Ireland as Eriksson's team attempted to maintain their fine form.
Minutes later, Leandro Damiao's header from Elano's corner clipped the top of the crossbar on its way out.
England battled hard against a superior Brazil, but Nilmar headed Elano's pass beyond Ben Foster after 47 minutes.
"I forgive as I am not a player that feels remorse but I believe referees should be much tougher, " said Elano.
Elano sought to change that trend with a back-post cross that was headed high over the top by Chelsea's Ramires.
But City were not done yet and Elano volleyed over from six yards before substitute Vassell somehow scored the winner.
But the injury is not as bad as first feared and Elano hopes to be fit for Brazil's final group game on Friday.
Onuoha headed Elano's corner over when he should have found the target and Pablo Zabaleta tested Zaza again from long range.
Real Madrid forward Kaka was suspended and midfielder Elano missing through injury, but Dunga said their absence did not hinder his side.
Elano was somehow running the game from right-back, picking out Vassell behind the defence and finding Petrov with some wonderful crossfield passes.
The 21-year-old is Eriksson's fourth signing in two days after deals for Javier Garrido, Vedran Corluka and Elano were completed on Thursday.
Brazil midfielder Elano made it 4-0 from the penalty spot just before an hour's play, then Ousmane N'Doye netted a consolation on 63.
The late goal glut was both unexpected and welcome, especially for City who had not managed a shot on goal until Elano's spot-kick.
That seemed to ignite the hosts with Elano to the fore and Emile Mpenza twice firing on goal, once on target and once wide.
Former Manchester City midfield man Elano split Wes Brown and Matthew Upson with a glorious pass and Nilmar arrived to direct a header beyond Foster.
Zaza did even better to stop Robinho's first-time shot after good work by Stephen Ireland, while Wright-Phillips was horribly off-target following another sublime Elano through-ball.
Blues manager Alex McLeish's grin was as broad as the Spaghetti Junction, but that lasted four minutes when Elano reduced the deficit from the spot.
The Croat ghosted into the six-yard box to meet Elano's whipped free-kick but the ball bounced up off his knee and flew over the bar.
The 19-year-old midfielder drove at the heart of the Villa defence after being put through by Elano and fired a tremendous low effort beneath Carson.
BBC: SPORT | Football | Premier League | Man City 1-0 Aston Villa
Nosworthy will feel he was harshly adjudged to have clipped Sturridge in the area but that did not stop Elano from despatching the resulting penalty.
The dangerous Blumer Elano reacted quickest to the Dane's failed clearance and played in Johnson who was denied by Carson who blocked the snap-shot with his face.
BBC: SPORT | Football | Premier League | Man City 1-0 Aston Villa
The former England striker ran on to Elano's pass and, although he failed to connect properly with his shot, he still got enough behind it to beat Gordon.
Elano's availability will be a big boost for coach Dunga as he is without without midfielder Kaka, who is suspended for one match following his controversial sending off against Ivory Coast.
Elano has been pivotal for Brazil, scoring a goal in both their Group G games so far as the South Americans booked their place in last 16 with a match to spare.
With 10 minutes remaining City shored up their defensive ranks with Michael Ball replacing Elano and the reinforced rearguard ensured Sunderland's hopes of a come back went up in smoke.
The goal composed Dunga's previously erratic side and they doubled the lead with 18 minutes left when Robinho slid a fabulous pass in for Elano to slot home from inside the area.
We have got Elano, Stephen Ireland and Nery Castillo, who can all play in the hole behind the main striker, and he plays the way that gets the best out of them.
The muted home support, who entertained themselves by roundly booing visiting boss and former Manchester United stalwart Roy Keane, had to wait 26 minutes before seeing Gordon tested with a bobbler from Elano.
The club also rejected overseas bids for key players like wingback Danilo and midfielders Marcos Arouca and Ganso, and Santos spent considerable money bringing home European-based Brazilian players like Edu Dracena, Ibson and Elano.
Eriksson made one alteration from the side which beat Sunderland, with Vassell replacing Sun Jihai and attacking midfielder Elano shifting to right-back, a position he has previously filled for Brazil and former club Santos.
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