The Gunners had been dominating for long spells in the second half before Arteta’s low, long-range strike in the 87th minute beat Joe Hart and handed the Londoners the three points.
Mario Balotelli, who was lucky not to be shown a red card in the first half for a high lunge on Alex Song, was eventually given his marching orders for a second bookable offence after clashing with Bacary Sagna late on.
The win hoists Wenger’s men into third place, two points clear of local rivals Tottenham Hotspur – and leaves City trailing league leaders United by eight points after the Red Devils beat Queens Park Rangers 2-0 earlier on Sunday.
“We have been consistent in the last two months and the performance reflects what we have produced in the last 10 games: quality, spirit and determination,” Wenger told the BBC.
“In the end we got the better of them. The goal came late but we deserved to win. Against a good team like City if you don’t score early it is always a test, we gave them very little.
“Every time we are in trouble someone finds something special and the confidence is very high. The job isn’t done yet.
“City have a chance still but it will be difficult. If you are eight points behind with six games to go they have to win every game. The closer you get the less likely it is that United will make mistakes. They can smell the stable.
“[Balotelli’s challenge on Song] looked a red card to me, it was a bad tackle.”
Arteta, meanwhile, warned his Arsenal team-mates against complacency in the remaining six games as they bid to secure Champions League football for next season.
“It’s really important for us as there are a few teams putting pressure on us for a place in the Champions League,” he said.
“We dropped points last week so this was a massive three points. It was a good goal against a good team who have spent a lot of money.
“The table is changing every Sunday and it will stay like that for the rest of the season, if we lose one game the fight is on again so we can’t take our foot off the pedal.”
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