Fellaini's goal earned Everton their first win in nine games
Marouane Fellaini's close-range header from Stephen Pienaar's cross sealed Everton's first win in nine games.
After a dismal first half, Bolton had the better of the second, much of it thanks to Gretar Steinsson, but his strikers failed to match his industry.
Joseph Yobo did well to deny Kevin Davies late on, and the game looked to be drifting to a goalless draw.
But at the death Pienaar found Fellaini, whose header hit the inside of the left-hand post before going in.
There were few chances worthy of the name for either side in a largely incident-free first half, characterised by poor final balls and off-target efforts from distance.
Most of Everton's threat came from the hard-working Mikel Arteta on the left, with Fellaini's physical presence causing problems for Bolton's defence, but Jussi Jaskalaainen's goal rarely came under direct threat.
A vital three points - Moyes
Mustafa Riga and Steinsson put in plenty of hard work for the home side, but Howard hardly had a serious save to make.
Bolton began the second half with more intent, but continued to be strangely lacking in punch in front of goal.
Matt Taylor had a great chance when Johann Elmander flicked a pass on to him just outside the box in the middle of the pitch, but he failed to connect properly and it went to waste as it dribbled wide, summing up the general standard of finishing.
Steinsson too had a great chance midway through the second half when he broke clear on the right and cut in to the box.
We deserved the win - Megson
But despite having four team-mates unmarked in the box, he had a shot himself and it was an easy take for the Everton keeper.
Late on, both Elmander and Riga both came close to catching the Everton defence napping, but the visitors did enough to keep the home side out.
And just as the clock was reaching the 90 minute mark, they were made to pay, as Everton's record signing was on hand to score his second goal of the week and claim an unlikely win for David Moyes's side.
Bolton manager Gary Megson:
"I thought we deserved to win. Territorially we were pressing most of the time but we couldn't find an opening.
"In the last 10 minutes we were too open in our desire to get the winner.
"If you look at statistics, we had more shots on goal and more corners, but the only one that matters is scoring."
Everton boss David Moyes on Marouane Fellaini's goal:
"I didn't see the goal coming because it was a game littered with mistakes.
"I even thought when Fellaini headed it that it was going to bounce out. But he's done it again.
"I think we've signed an up and coming star of the future. If you ask anybody in Belgium, they will tell you exactly what they think of him."
BBC Sport Player Rater man of the match on 90 minutes: Everton's Marouane Fellaini 8.07 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
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