Mikel Arteta's brilliant strike on the hour gave Everton their first win in five games after a pulsating encounter.
Everton's Leon Osman shrugs off Bolton defender Henrik Pedersen
Arteta ended a solo run with a 25-yard drive that left Bolton keeper Jussi Jaaskelainen helpless.
Bolton were unfortunate not to claim a draw, with former Everton winger Idan Tal hitting a post and also forcing a fine save from keeper Tim Howard.
Ivan Campo was off target with two headers, but Arteta's goal was worthy of winning any game.
Everton were without top scorer Tim Cahill, ruled out with a knee injury, allowing James Beattie to make a rare start.
And Bolton had to do without midfield man Kevin Nolan, who has just become a father.
The first 45 minutes was a typically attritional affair, with both sides showing plenty of commitment but little quality.
But all that changed after the break, with Bolton in the ascendancy and Everton defending bravely.
Arteta broke the shackles to claim the points, but Bolton will feel they deserved at least a share of the points.
Bolton almost took the lead after 20 minutes when Tal's free-kick drifted on the wind, forcing keeper Howard to re-adjust and make a fine save.
Arteta was Everton's most influential performer, sending in a cross which Beattie glanced wide, then firing in a low drive which brought a solid save from Bolton keeper Jaaskelainen.
Bolton had opportunities of their own, with Campo heading wide after good work on the flanks by the tireless Kevin Davies.
And captain Gary Speed almost put Bolton ahead in freakish fashion four minutes before the interval, when he headed Howard's clearance back towards an empty net, but was just off target.
Joseph Yobo then had Everton's best chance in first-half injury time, but he shot over when unmarked.
Tal, hoping to make a success of his second crack at the Premiership, almost broke the deadlock after 50 minutes, but his volley was inches away with Howard beaten.
El-Hadji Diouf, as ever receiving fearful abuse from the opposition crowd, almost silenced the taunts with a twisting run and shot that was blocked by Alan Stubbs.
Everton ended the stalemate on the hour with a goal of stunning quality from Arteta.
He advanced on goal and shrugged off two Bolton challenges before sending a rising drive beyond Jaaskelainen from 25 yards.
Bolton, who had just enjoyed their best spell of the game, were stung into action, with Campo heading just over and the unfortunate Tal hitting the post with a low shot.
The visitors were unlucky to be behind, with Speed bringing another excellent block from the busy Howard.
Everton manager David Moyes:
"Mikel Arteta scored a very special goal and we are delighted.
"It was terrific. I said we needed other people to step forward and get us goals with Tim Cahill out, and that is what Mikel has done.
"Any game against Bolton is always going to be hard and they made it really difficult. The game could have gone either way and it took a wonder goal to settle it."
Bolton manager Sam Allardyce:
"I don't just feel disappointed, I feel robbed - that is the answer I would give you about that game.
"We had complete control of this game from start to finish and squandered so many opportunities. We then just had one slip at the back - and we were punished by what was admittedly a terrific strike from Mikel Arteta.
"I would have been disappointed with a draw, so I am gutted to be going away without anything."
Everton: Howard, Yobo, Stubbs, Lescott, Nuno Valente, Osman, Carsley, Neville, Arteta, Johnson, Beattie (Anichebe 76).
Subs Not Used: Wright, Weir, Van der Meyde, Vaughan.
Booked: Neville, Anichebe, Johnson.
Goals: Arteta 60.
Bolton: Jaaskelainen, Hunt, Ben Haim, Meite, Pedersen, Tal, Campo (Giannakopoulos 83), Speed (Faye 90), Davies (Vaz Te 90), Anelka, Diouf.
Subs Not Used: Walker, Fortune.
Ref: U Rennie (S Yorkshire).