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Owen Coyle's side trailed to an early goal from Dave Kitson but Taylor struck twice in the last five minutes to lift Bolton seven points clear of the relegation zone.
Third bottom Hull would have to win three of their last four matches to catch Wanderers, who look certain to beat the drop.
Stoke boss Tony Pulis opted to leave Matthew Etherington on the bench after the winger suffered a knee injury during the week.
But the hosts were on top from the start and took the lead in the 13th minute as Tuncay Sanli lofted the ball over the Bolton defence for Kitson to flick past Jussi Jaaskelainen before slotting into the empty net.
Rory Delap caused more problems for Bolton with a trademark long-throw that Robert Huth met with a header which cannoned back off a post and deflected to safety.
Tuncay cleverly won a corner just before the break but Huth was only able to head the resulting set-piece straight at Jaaskelainen.
Coyle tried to inject more urgency into his side's attack by throwing on striker Ivan Klasnic at half-time.
And the visitors had a chance within seconds of the restart when Kevin Davies nodded down Paul Robinson's free-kick, only for Zat Knight to shoot woefully wide.
Wanderers went closer moments later as Davies squared to Klasnic, who flashed his shot just wide.
Bolton seemed to be growing in confidence and Matt Taylor and Klasnic tried their luck from long-range before Jack Wilshere, on loan from Arsenal, forced Sorenson into a good save.
Stoke still should have put the game to bed as Etherington surged down the left flank and played the perfect pass for Tuncay, who hit the post from close-range. Kitson fared even worse as he lifted the rebound over the crossbar.
Those narrow escapes gave Bolton the belief to make one last push and they equalised in the 85th minute after substitute Vladimir Weiss was brought down by Dean Whitehead on the edge of the area.
Taylor took full advantage as he rifled the free-kick past Sorenson into the bottom corner.
That was the signal for a remarkable finish as Taylor converted a cross from Weiss in the 88th minute to spark wild celebrations among the travelling fans.
