Taylor buried his first with a sweetly struck 20-yard free-kick after substitute Vladimir Weiss was adjudged to have been tripped by Dean Whitehead.
Stoke were furious as the Slovakian seemed to dive and it took referee Stuart Attwell, a late replacement for Martin Atkinson who was switched to the Manchester derby, some time to award the infringement.
Taylor wasn't asking any questions as he blasted a low shot underneath the defensive wall and out of Thomas Sorensen's reach with five minutes remaining.
And Taylor sent around 2,000 travelling fans into ecstasy when he stuck out a leg to divert in a right-wing cross from Weiss two minutes later.
The drama wasn't quite over as Stoke captain and former Bolton centre-back Abdoulaye Faye squandered a gilt-edged chance to earn his side a point in stoppage time.
Robert Huth's header fell straight into his path three yards from goal, but Faye somehow hooked his shot over the top when it looked easier to score.
Taylor curled a second minute free-kick against the defensive wall, but Stoke soon clicked into gear as Huth headed over before the home side took a 13th minute lead.
It was a terrific goal as well with Glenn Whelan sliding a pass to Tuncay before the Turkey international played a delightful ball into the path of strike partner Dave Kitson.
Kitson timed his run to spring the Bolton offside trap and he took the ball around the unguarded Jussi Jaaskelainen and tucked away his eighth goal of the season.
Huth then headed a long throw from Delap against a post, with Liam Lawrence close to knocking in the rebound, as Bolton struggled to stay in the contest.
Stoke's confidence was now overflowing as Tuncay and Whelan, in particular, were involved in some excellent passing moves which belied their stereotype as a long-ball team.
And Bolton, who had not forced Sorensen into a meaningful save, could consider themselves fortunate to reach half-time with only a single goal deficit.
Owen Coyle had seen enough and decided on a positive change with midfielder Sam Ricketts making way for Ivan Klasnic.
The Croatian striker gave the isolated Kevin Davies some much needed support and both players went close to equalising within five minutes of the restart.
Davies had a shot blocked in front of goal by Faye, before Klasnic went even closer when he fired Taylor's cross inches wide.
It was a much different game now and Stoke also needed some dogged defending, including a couple of last-ditch tackles, to keep the visitors out.
But they managed to ride the storm and hit back strongly as Jaaskelainen saved well from Dean Whitehead after an inch-perfect pass from Kitson played in the midfielder.
It should have been 2-0 17 minutes from time when Tuncay shot against a post from a pin-point low cross by substitute Matthew Etherington.
And Taylor made Stoke pay as Bolton's smash-and-grab finish eased them a healthy seven points clear of the bottom three.