Wanderers went in front mid-way through the second half thanks to a strike from Johan Elmander.
The Baggies responded well, though, and drew level in the 78th minute when James Morrison nodded in Peter Odemwingie's cross.
Both sides went into the contest looking to build upon impressive results from the previous weekend, but neither were able to make the breakthrough in a tightly-contested opening period.
The hosts carved out the first opportunity of the game in the second minute with Chris Brunt swinging an inviting ball into the box which Morrison was only just unable to get on the end of.
Bolton had a chance of their own soon after but skipper Kevin Davies could not get any real power on his header from Lee Chung-yong's cross and the ball bounced into Scott Carson's arms.
Gary Cahill, back in the Wanderers team after serving a three-match suspension, made a better connection with Martin Petrov's corner having been allowed the space to do so, but the England defender's header went narrowly over the bar.
At the other end, Brunt tried a speculative effort from distance which was deflected wide and Jussi Jaaskelainen punched away the resulting corner from the same player.
Baggies frontman Odemwingie, named as the Premier League's player of the month for September, then turned on the edge of the area and drilled a low shot off target.
The Nigeria forward was looking to add to his tally of three goals in five games since joining Albion in August and made another attempt just before the half-hour mark with a header that he could not keep down.
Brunt was next to try his luck with a swerving strike that bounced off Jaaskelainen.
Elmander then flicked a cross into the West Brom box which Jonas Olsson just managed to nod away before it reached Davies, and Gretar Steinsson got his head to a Petrov corner but Carson caught the ball comfortably.
Bolton started the second half in purposeful fashion and after Carson had tipped away an effort from Petrov, Cahill saw his header cleared off the line.
Davies then hit a shot that Carson managed to deal with, but the visitors were looking threatening and in the 64th minute they took the lead.
A neat build-up led to Davies laying the ball into the path of Elmander, who broke into the box and finished to notch his fourth goal of the season.
Odemwingie had a great chance to equalise after pouncing on an error by Zat Knight, but he dragged his shot disappointingly wide.
The forward soon made amends, though, showing some tidy footwork before flighting a wonderful cross for Morrison, who headed home to make it 1-1 with 12 minutes of normal time remaining.
Moments later Odemwingie teed up another opportunity by squaring to Brunt, but the midfielder was denied by a brilliant save from Jaaskelainen.
Substitute Matthew Taylor did his best to try and put Bolton back in front but his free-kick was just too high and he then flashed a strike across goal and wide.
Odemwingie found himself in a good position again in the dying moments but could not bring the ball under control.