Marouane Fellaini headed home in the last minute to give Everton their first win in nine games and heap more misery on under-fire Bolton manager Gary Megson.
The Toffees' record £15million buy from Standard Liege followed his equaliser against Manchester United by scoring from a Steven Pienaar cross.
Pienaar and Fellaini both looked suspiciously offside but the goal was given and furious Trotters fans booed off their team, who have now failed to win at home since the opening day of the season.
Megson suffered verbal abuse from a section of supporters during Sunday's 2-0 defeat at Tottenham and this latest setback will place the former West Brom boss under further scrutiny.
The Trotters created next to nothing and Megson's decision to splash out a club record £8.2million on Johan Elmander again looked seriously ill judged.
The Sweden striker arrived from Toulouse during the summer but was virtually anonymous throughout and never came close to adding to his solitary goal for the club.
Bolton look destined for a relegation dogfight but Everton boss David Moyes had reason to smile thanks to Fellaini's late heroics.
After the creditable 1-1 draw at home to United on Saturday, Moyes resisted the temptation to hand Tim Cahill an immediate recall. The Australia international was available after a three-match ban and entered the action in the 63rd minute, but did not have much chance to shine.
Bolton were without former Everton man Gavin McCann, suspended after being sent off at Tottenham, and his midfield berth went to Dutch winger Riga.