Dave Kitson had given the Potters a first-half lead after latching onto Tuncay Sanli’s pass and rounding Jussi Jaaskelainen in the 13th minute.
But Taylor turned the match around, drawing things level with a free-kick in the 85th minute before netting the winner three minutes later.
The win takes Owen Coyle’s side – who had lost their previous four matches – up to 14th in the Premier League, but more importantly, they are now seven points clear of the drop zone with three games to play.
It was a result that looked unlikely after a first half which Stoke dominated.
The hosts’ first chance came in the 11th minute when Rory Delap almost crept in to steal the ball as Gretar Steinsson attempted to shepherd it back to Jaaskelainen.
After it was scrambled away, Delap launched his first long throw of the game into the Wanderers’ box which Robert Huth sent looping over the bar.
Two minutes later, the Potters were ahead as Tuncay lofted the ball over the Bolton defence for Kitson, who prodded it past a stranded Jaaskelainen before slotting home.
Stoke almost doubled their advantage shortly after as another long throw was again met by Huth, whose header hit the post before bouncing off Liam Lawrence and out of play.
Fabrice Muamba picked up a yellow card on the half-hour after clattering Huth, but from a handy position, Glenn Whelan could only blast the free-kick into the Bolton wall and the ball was cleared.
A minute later, Tuncay picked out Kitson again with another delightful pass, but as the former Reading striker advanced towards Jaaskelainen he was flagged offside.
Tuncay created some space for himself in the area five minutes before the break but was denied by a slide tackle from Paul Robinson, and Huth made a poor connection when the ball fell to him from a corner, leaving an easy catch for Jaaskelainen.
Having seen his side produce next to nothing in the opening 45 minutes, Coyle tried to inject more urgency into the Bolton attack by throwing on striker Ivan Klasnic for the second half in place of Sam Ricketts.
The visitors looked determined to make a better go of things and had a chance within seconds of the restart when Kevin Davies nodded down Robinson’s free-kick in the box, but it fell to Zat Knight, who produced the finish of a centre-half which was well off target.
Five minutes later Wanderers had their best opportunity so far as Davies squared to Klasnic, who flashed a shot across Thomas Sorensen’s goal that went the wrong side of the post.
Taylor then blazed his attempt at a spectacular volley high over the bar before finding Klasnic, who again could only send his effort wide.
Bolton seemed to be growing in confidence and on the hour Klasnic instigated a counter-attack which led to Jack Wilshere forcing Sorensen into a diving save.
Stoke were looking a shadow of themselves in the first half, but Danny Collins did get a header away in the 66th minute that did little to trouble Jaaskelainen.
The Potters had been on the ropes for most of the half, but with 20 minutes to go they suddenly created a flurry of chances that could have sealed the game.
First Dean Whitehead bolted forward and attempted to hoist a long ball over Jaaskelainen, but the Finnish keeper jumped to palm the ball upwards and the danger was cleared.
Then substitute Matthew Etherington surged down the left flank and played the perfect pass for Tuncay, who hit the post from only a few yards out.
Kitson was perhaps even more guilty of profligacy immediately after as he hit the rebound over the bar under a challenge from Steinsson.
Stoke were back in the ascendancy and eager to seize the moment, Tony Pulis sent on Ricardo Fuller for Tuncay.
Moments later Jaaskelainen was tested again as Danny Higginbotham sent a low drive into his arms, and Kitson then headed over from Etherington’s corner.
It was Kitson’s final act as Pulis put on James Beattie to add more fresh legs up front, but it was Bolton who hit back with five minutes remaining after their substitute Vladimir Weiss was brought down by Dean Whitehead on the edge of the area.
Taylor rifled the free-kick past Sorensen into the bottom corner and Wanderers were level.
Three minutes later Taylor was the matchwinner as he got on the end of Weiss’ cross, before Stoke captain Abdoulaye Faye wasted a glorious chance to equalise at the death.