As Sunderland fans celebrated wildly at the final whistle, Villa's supporters rounded on Martin O'Neill's side as their recent indifferent form continued.
Sunderland suffered a blow before kick-off when influential striker Kenwyne Jones was ruled out through illness, while Villa's only change was the recall of Craig Gardner for suspended Olof Mellberg.
John Carew almost gave Villa the perfect start after four minutes when he produced a surprise overhead kick which flew narrowly wide with Sunderland keeper Craig Gordon motionless.
But Sunderland more than held their own in the first 45 minutes, with Villa's cause not being helped by a shaky performance from England keeper Carson.
He was fortunate to escape in the 23rd minute when he dropped a long ball and appeared to handle outside the area as he attempted to retrieve the situation, but referee Howard Webb ignored Sunderland's appeals.
O'Donovan should have put Sunderland ahead three minutes later when he directed a poor header well over the bar when unmarked only eight yards out.
Carew was at the centre of most of Villa's attacking threat, and he almost broke the deadlock four minutes before half-time when he pounced on a poor clearance from Gordon, but the Sunderland keeper recovered to save his shot on the turn.
Sunderland were furious with referee Webb again on the stroke of half-time when Andy Reid's shot struck Nigel Reo-Coker on the arm, but once more their claims were waved away.
Villa boss O'Neill made a bold substitution after 56 minutes, sending on striker Harewood for holding midfield man Reo-Coker - a move that almost yielded instant dividends.
Harewood muscled Sunderland defender Nyron Nosworthy out of the way, but steered his first touch of the game inches wide with only Gordon to beat.
He was a lively presence after his introduction, unsettling the Sunderland defence again only to find the side-netting.
Sunderland still looked dangerous on occasion, and Grant Leadbitter wasted a good opportunity to put them ahead with 13 minutes left, dragging his shot across the face of goal when well-placed.
But Sunderland got the goal their determination and resilience deserved after 83 minutes, when Richardson's speculative long ball dropped behind Zat Knight, leaving Chopra to race clear and coolly loft a finish over Carson.
Villa almost responded instantly when Gabriel Agbonlahor broke into the area, but Gordon saved with his legs to clinch a priceless victory.
Aston Villa boss Martin O'Neill: "We failed to take any chances that came our way but you can't just point the finger at that.
"Our overall play was disappointing and it is my responsibility. Since we drew with Arsenal a fortnight ago we have been really disappointing.
"You would not expect us to collect only one point from our last two home games. I have to rectify it."
Sunderland boss Roy Keane on their first away victory of the season: "We have been unlucky in some away games - it is not as though we have been battered every week.
"We have played quite well without getting over the finishing line but here we achieved it.
"We played some decent stuff. Maybe we rode our luck a little bit but we got one clear-cut chance in the second half and managed to take it."
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