The midfielder held his nerve to cancel out Dave Kitson's 53rd-minute opener after Danny Collins' clumsy challenge on Sam Ricketts just inside the area.
In a largely forgettable encounter, Gary Cahill had the afternoon's first chance but the defender headed over from Tamir Cohen's cross on 20 minutes.
The game's flow, or lack of it, was not helped by a succession of stoppages, mostly for head injuries which should come as no surprise as the ball spent most of the opening period in the air.
Indeed, at times the Reebok more resembled a casualty department at a hospital than a football pitch, as several dazed players wandered round clutching their heads.
The one bright spark of a terrible first half was provided by Glenn Whelan's curling free-kick but Jussi Jaaskelainen was equal to it on 33 minutes.
So poor was the match, Bolton fans started a slow hand-clap towards the end of the first half - surely a first at a football match - before booing their side off at half-time.
Megson introduced new signing Ivan Klasnic and Ricardo Gardner at the interval in a bid to give Wanderers some much-needed impetus going forward.
And it nearly paid off immediately when the two combined to play in Taylor but he volleyed wide on 62 minutes.
Less than 60 seconds later, Stoke were ahead. Ricardo Fuller beat Cahill in the air to win the flick-on, and Kitson brushed off Ricketts' weak challenge before curling into the bottom corner.
Only a superb save from Thomas Sorenson denied Klasnic a goal and, from the resulting corner, Zat Knight should have equalised but blasted over after the ball had dropped to him on the edge of the six-yard box on 69 minutes.
Fuller could have settled the contest moments later but his shot lacked the power to trouble Jaaskelainen.
And Taylor made Stoke pay when he stepped up to coolly send Sorenson the wrong way in the final minute.