Joleon Lescott's last-gasp header gave Everton victory after record buy Yakubu marked his debut with a goal.
Yakubu made a scoring start to his Everton career
The £11.25m striker rounded off a brilliant counter-attack by turning in Andrew Johnson's pass after 11 minutes.
Mikel Alonso hit the bar with a rising drive before Nicolas Anelka deservedly drew Bolton level with a powerful volley after 55 minutes.
Everton, inspired by substitute Thomas Gravesen, snatched the points when Lescott headed home the Dane's corner.
Boss David Moyes gave first Premier League starts to Everton's summer signings Phil Jagielka and Steven Pienaar, with Gravesen on the bench.
And the tiny South African was involved in the sweeping move that saw Everton go ahead after 11 minutes.
Pienaar found Johnson, who sped past Gerald Cid before finding Yakubu perfectly at the far post, who swept home a simple finish.
Bolton responded with predictable defiance, with El-Hadji Diouf posing problems to the Everton defence on both flanks.
Alonso produced a range of shooting that bore comparison with his more illustrious brother Xabi, and was desperately unlucky not to draw Bolton level.
He produced a magnificent save from Tim Howard with a rising drive, then an even better effort rebounded to safety off the bar six minutes before the interval.
Bolton were forced into a change at half-time, Andy O'Brien replacing the injured Cid.
Anelka was also a threatening figure, and he gave Bolton a deserved equaliser after 55 minutes.
Diouf's cross was only half-cleared, and Anelka thumped a rising volley past Howard.
Anelka then set up Kevin Nolan at the far post, but he wastefully side-footed wide when he looked certain to score.
Everton were very much on the back foot, so boss Moyes threw Gravesen into the fray in place of Carsley.
Alonso was shooting at every opportunity, forcing Howard to save low down with another powerful effort.
Gravesen's arrival gave Everton a measure of control, and Pienaar was narrowly off target from 10 yards.
The Dane then released Johnson, but Bolton keeper Jussi Jaaskelainen made a vital block.
Abdoulaye Meite tested Howard with a header from a corner as both sides pushed for the winner.
Gravesen then brilliantly created an opening by sending in Mikel Arteta, but substitute Leon Osman shot high over the bar.
And he was involved again as Everton took the lead in dramatic fashion with 90 seconds left.
Gravesen's corner was met at the far post by Lescott, who headed home powerfully.
The Dane celebrated wildly with Everton's fans at the final whistle as they celebrated a dramatic late winner.
Bolton manager Sammy Lee:
"I've told the players that if they keep that level of commitment we will turn this around.
"There have been a lot of malignant rumours about the commitment and the dressing room at this club, but anyone who saw that performance will see for themselves that it's not true.
"It was very disappointing to concede a late goal from a set-piece, because we pride ourselves on that. We want to get a clean sheet mentality here, but we haven't got it yet, but I am confident we will starting getting the results we deserve soon."
Everton manager David Moyes:
"Thomas Gravesen made a massive difference to us when he came on.
"He brought a calmness to us and made us play better. He's lacking a bit of fitness but he made some killer passes that helped us win the game.
"It was great for Yakubu to get off the mark, but huge credit must go to Andy Johnson - that was a real strike partnership goal."
Bolton: Jaaskelainen, Hunt (Davies 80), Meite, Cid (Andrew O'Brien 46), Samuel, Speed, Nolan, Alonso, McCann (Wilhelmsson 56), Diouf, Anelka.
Subs Not Used: Al Habsi, Braaten.
Goals: Anelka 55.
Everton: Howard, Jagielka, Yobo, Lescott, Baines, Arteta, Neville, Carsley (Gravesen 61), Pienaar (Osman 70), Yakubu (Anichebe 84), Johnson.
Subs Not Used: Wessels, McFadden.
Booked: Baines, Lescott, Gravesen.
Goals: Yakubu 11, Lescott 90.
Ref: Peter Walton (Northamptonshire).