Joleon Lescott’s last-gasp header gave Everton victory after record buy Yakubu marked his debut with a goal.
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.
Younes Kaboul poked home after Antti Niemi had flapped at Gareth Bale’s corner and Dimitar Berbatov smashed in Robbie Keane’s sublime flick.
Saha headed in at the near post from Nani’s corner with 18 minutes to go after former United favourite Keane’s side had frustrated the champions. 
