Mark Hughes' side looked to be heading for defeat when, trailing 3-2, Craig Bellamy was given his marching orders in controversial circumstances on 65 minutes.
But the Argentina hitman struck a wonderful 77th-minute equaliser to earn the visitors an eighth draw in nine Premier League games.
Wanderers looked anything but a side who had lost five of their previous six games, as they flew out of the blocks.
And the hosts were ahead on 11 minutes when Ivan Klasnic struck from close range when Chung-Yong Lee's shot took a deflection off Sylvinho into the Croatian's path.
City were level on 28 minutes though when Tevez's effort from the edge of the area clipped Tamir Cohen to wrongfoot Jussi Jaaskelainen.
That goal galvanised the big-spending visitors and Gareth Barry wasted a great chance when he drilled wide moments later.
But it was Bolton who went back in front two minutes before the interval when defender Gary Cahill curled home a wonderful strike from 20 yards.
But the hosts couldn't hold on to their lead after Micah Richards drove on to Bellamy's delightful pass to finish off a flowing City move in first-half injury time.
The goals continued after the restart when Klasnic reacted superbly to volley home Davies' flick-on from Paul Robinson's cross on 53 minutes.
The game then turned even more in Bolton's favour when Bellamy was dismissed. The City forward was booked for a dive and then, presumably, must have said something to referee Mark Clattenburg because a red followed immediately afterwards.
But the outstanding Tevez came to the rescue when he rifled home with just 13 minutes remaining to extend City's 11-game unbeaten run.