For City it was a devastating night as a win would have narrowed the gap to the south coast side to one point with a game in hand.
But for a long spell in the second half they were simply outplayed as the goals were carved out.
O'Connor scored the first on the hour, steering his shot home with the outside of his right boot after the opening had been schemed by Wade Elliott and Steve Fletcher.
His second and 14th of the season came from the penalty spot after centre-back Danny Coles had been booked for flooring John Spicer.
The Dubliner had missed a penalty a fortnight ago but stroked this one calmly into the far corner of the net to give Bournemouth a history-making run of success - never before had they won five away games on the trot.
For the first quarter it had been all City. As they pressed forward Neil Moss had to pull off an alert save to keep a 25-yard shot from young Scott Brown from entering the net.
But after 15 minutes Louis Carey gave away a free-kick 15 yards into his own half. The ball broke to Matthew Mills and his low drive hit the base of a post.
There was more anxiety for City as goalkeeper Steve Phillips turned away a searing drive from Brian Stock.
From the corner Stock again tested Phillips, but then as City struck back, Moss brought off saves under his bar from both Stephen Brooker and Coles.
The tempo showed no sign of slackening and Brooker won a series of free-kicks around the box, but when Bournemouth moved forward they had an added urgency as a unit.
Stock was running the midfield sharply, bringing Spicer on his left into the game at every opportunity.
Early in the second half City passed up a good scoring chance when a Brooker flick put Leroy Lita clear. With Moss coming out to narrow the angle, Lita hurried a shot over the bar.
The miss took on greater importance when Bournemouth broke through on the hour to break the deadlock decisively.