Second-half substitute John Heitinga’s injury-time strike snatched victory for Everton in Wanderers' fourth round FA Cup clash at the Reebok.
The tie looked set to end all-square after Marvin Sordell’s 27th-minute strike had cancelled out Steven Pienaar’s fortuitous goal nine minutes previous.
Both Marcos Alonso and Chris Eagles went close in the second period before Heitinga’s late effort ensured that David Moyes’ side will advance to the next round.
Dougie Freedman made four changes from last weekend’s goalless draw at Crystal Palace as Andy Lonergan, Sam Ricketts, Josh Vela and Marvin Sordell returned to the starting line-up, while Adam Bogdan, Tyrone Mears, Keith Andrews and Kevin Davies all missed out.
Groundstaff worked through the night to get the game on and 18,760 supporters braved the adverse weather conditions and it was the visitors who created the game’s first opportunity.
Nikica Jelavic found space down the right flank, but his dangerous cross could only be diverted wide of Lonergan’s far post by the onrushing Pienaar.
The Toffees enjoyed the best of the opening exchanges, as Kevin Mirallas went close from a free-kick on the edge of the area before Jelavic’s close-range effort was superbly blocked by the sliding Tim Ream.
But Moyes’ side took the lead after 18 minutes in somewhat fortuitous fashion. Leighton Baines’ cross from the left wing was hit first time by Jelavic and the ball ricocheted of Pienaar and past the helpless Lonergan to give the Blues an early lead.
Wanderers enjoyed a good spell of possession soon after as Chung-Yong Lee headed Jay Spearing’s corner narrowly wide, before the Trotters levelled the scores in the 27th minute.
Ricketts made space down the right and fed Darren Pratley whose first-time ball across goal fell to the feet of the in-from Marvin Sordell who clinically slid the ball past the outstretched Tim Howard.
The Whites were in the ascendency and almost took the lead minutes later. Eagles weaved his way past a couple of Everton defenders and found Pratley on the edge of the box, but his powerful strike was well saved by keeper Howard.
Victor Anichebe almost snatched a second goal for the visitors soon after, but the forward could only guide Phil Neville’s cross wide of goal.
Wanderers ended the first half on top as first Eagles tested Howard from range before Lee chipped an effort on the edge of the area inches wide as the scores remained level at the break.
The Whites continued from where they had left off at the start of the second half as Howard was forced into an early save from the marauding Alonso who struck a vicious low shot but couldn't beat the Everton stopper.
The Trotters enjoyed the large share of the early second-period possession, but the Toffees were dangerous on the counter attack and Jelavic almost found a way through on goal but was denied by the onrushing Lonergan.
Both teams continued to push forward as Pienaar’s chip on the edge of the Bolton area went narrowly over the top before Eagles saw an attempt go past Howard’s far post.
Lonergan produced a superb goal-saving stop soon after. Pienaar was able to find space inside the Whites’ penalty area, and his low strike was pushed wide by the diving Bolton stopper.
But Everton would snatch a late winner after Wanderers defence failed to clear a Toffee’s corner and the ball finally made it’s way to Heitinga who smashed the ball past Lonergan.
Wanderers: Lonergan, Ricketts, Knight, Ream, Alonso, Vela (Holden 81), Spearing, Eagles (Afobe 74), Pratley (Ngog 85), Chung-Yong, Sordell (Unused Subs: Bogdan, Mears, K Davies, C Davies)
Everton: Howard, Neville, Baines, Jagielka, Distin, Mirallas (Gueye 17), Pienaar, Osman, Fellaini, Anichebe, Jelavic (Heitinga 80) (Unused Subs: Mucha, Oviedo, Naismith, Vellios, Duffy)