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The former Sunderland player, who joined Villa on Tuesday in a club-record deal, broke the deadlock with his first clear-cut opportunity after 18 minutes.
With their £59million strike force of Carlos Tevez and Edin Dzeko, the visitors dominated for long spells, but they struggled to find a way past Villa's rock-solid defence in which James Collins and former City centre-back Richard Dunne were outstanding.
The result means City are now three points behind Premier League leaders Manchester United, having played two games more.
Villa held on to register only their second win in 11 league games and it lifted them further away from the bottom three.
It also gave them revenge for a 4-0 mauling at Eastlands last month.
Villa had a let-off after 16 minutes when an inswinging corner from Aleksandar Kolarov caused problems, but neither Dzeko nor Tevez could apply the decisive touch from close range.
After 18 minutes, Villa Park erupted when Bent converted his first chance for his new club.
Gabriel Agbonlahor found Ashley Young in space and his curling effort was parried aside by Joe Hart. But Bent was first to react to the rebound and slotted it into the corner of the net.
City tried to retaliate and Brad Friedel produced a fine save to tip Vincent Kompany's header over the crossbar from Kolarov's corner.
Ciaran Clark became the first player to be yellow-carded after bringing down Dzeko.
Young then almost picked out the late run of Bent with a fine pass but the ball skidded off the surface.
Hart was also alert to cut out a similar ball from Agbonlahor aimed at the former Sunderland player.
Former Villa captain Gareth Barry went close to bringing City level after 37 minutes when his glancing header slid past the far post from Jerome Boateng's threatening ball into the box.
Young got plenty of power behind a low 20-yard drive in the last minute of the first half, but Hart had his body behind the ball.
City continued to press at the start of the second period. Collins blocked a shot from Dzeko after the striker had cut inside following good play by David Silva.
Dzeko got on the end of a corner from Kolarov, although he could not keep his header down.
City boss Roberto Mancini made his first change after 57 minutes with Adam Johnson replacing Barry, who was jeered by home fans as he left the pitch before Collins again did well to block a drive from Tevez.
Friedel then knew little about keeping out a powerful low drive from Boateng, which bounced off him and away to safety.
Dzeko looped a header past the post as the pressure increased from the visitors.
At the other end, Hart was called into action to turn a dipping drive from Young away for a corner.
Kolarov was booked after 69 minutes for bringing down Marc Albrighton before Cuellar threw his body in front of a drive from Dzeko to typify Villa's fighting spirit.
Downing cut in from the right, but his rising effort did not over extend Hart.
Collins produced another superb block to deny a Tevez volley as the game entered the final 10 minutes and Clark deflected a 25-yard shot from De Jong against a post with Friedel stranded.
Then Dzeko headed wide from close range when it seemed easier to score.
In a rare Villa attack, Young poked the ball wide at the near post from Albrighton's cross, but one goal was enough.