Second-half goals from Marouane Fellaini and Apostolos Vellios condemned Bolton to their 10th league defeat of the season.
The home side were reduced to 10 men after just 20 minutes when David Wheater was sent off for a challenge on Diniyar Bilyaletdinov.
Fellaini broke the deadlock when he got on the end of a cross from Leighton Baines to poke home from close range.
Vellios then made sure of the points by smashing home from six yards out.
It could have been so much more convincing for David Moyes' side, who at times struggled in front of goal.
Tim Cahill was, once again, guilty of spurning chances but in the end it did not matter.
It was never going to be easy for Bolton, who, before the match, had lost five of their last six home games.
The task got even harder when they were reduced to 10 men when Wheater was sent off for the second time this season.
A poor touch by the former Middlesbrough defender took the ball away from him and he jumped in on Bilyaletdinov on the halfway line, leaving referee Michael Oliver no option but to show the red card.
Mark Davies was the man who moved into defence, which allowed the visitors free rein in midfield.
Despite dominating the possession, though, Jussi Jaaskelainen was forced into just one save before the break.
A well-worked free-kick on 37 minutes saw Johnny Heitinga curl a low effort around the wall but the Bolton keeper got down well to his left to make the save.
Did you know?
- The win was Everton's first at the Reebok Stadium since 2008
- Vellios has scored three times this season after coming on as a substitute
- Fellaini's goal was his third against Bolton at the Reebok Stadium
Whatever Moyes said at half-time did the trick because it took just four minutes for his side to break the deadlock.
Leon Osman moved the ball out to Leighton Baines on the left and he played it in first time. Fellaini got ahead of the Bolton defence to poke home from close range for his first Premier League goal of the season.
The visitors continued to press, with Baines causing Wanderers all sorts of problems down the left.
Bilyaletdinov also went close but he could only drive straight at Jaaskelainen, before Louis Saha shot straight down the throat of the Bolton keeper.
At the other end the home side created their best chance of the match, when Mark Davies played a lovely through ball for Ivan Klasnic. He got the better of his marker but Tim Howard stood firm and saved with his feet.
That chance proved to be their last real hope as Everton went in search of a second goal, only Jaaskelainen preventing them from adding to their tally.
The Finn made a good double save on 71 minutes, first blocking a shot from Cahill before recovering to make a second save from Saha with the rebound.
It was all over for Bolton with 12 minutes to go when Everton doubled their lead courtesy of Vellios, on as a second-half substitute.
Baines was again the provider as he hit a long pass for Cahill at the far post. The Australian hooked the ball back across the goal and Vellios, arriving from the left, fired home.
Bolton boss Owen Coyle: "David took a bad touch, there is no getting away from that, and he tried to recover it.
"I think the rules are in place that if your studs are showing, you leave yourself wide open to a red card and watching it in real time, I certainly feel he did lead with his studs.
"If he has caught the lad, then the referee is in a difficult place with regard to the rules, which they have to abide by."
Everton manager David Moyes: "We have been slow starters in the past, although I didn't actually think we had started slow this year.
"We lost the first game, but we got a few points on the board.
"Then we had a run of fixtures with a lot of the big teams in a row, but I hope this is the start of us picking up, because we normally do and when we do, we tend to stay on it and go with it."
Live Text Commentary
Full Time The referee brings the game to a close.90:00 +2:18
Ross Barkley takes a shot. Blocked by Mark Davies.90:00 +0:30 Substitution
Substitution Magaye Gueye on for Diniyar Bilyaletdinov.90:00 +0:30
The referee blows for offside. Zat Knight restarts play with the free kick.89:59
Ross Barkley has an effort at goal from 25 yards. Blocked by Gretar Rafn Steinsson.88:02
Ivan Klasnic is ruled offside. Free kick taken by Johnny Heitinga.87:04 Substitution
Substitution Ross Barkley is brought on as a substitute for Tim Cahill.86:44
The ball is crossed by Gretar Rafn Steinsson, Leighton Baines gets a block in. Blocked by Leighton Baines.85:58
Gretar Rafn Steinsson takes a shot. Johnny Heitinga gets a block in.85:24
Marouane Fellaini gives away a free kick for an unfair challenge on Chris Eagles. Indirect free kick taken by Paul Robinson.84:28
Tuncay Sanli challenges Leighton Baines unfairly and gives away a free kick. Free kick taken by Johnny Heitinga.81:16
Free kick awarded for a foul by Leighton Baines on Gretar Rafn Steinsson. Free kick taken by Jussi Jaaskelainen.80:07
Apostolos Vellios produces a right-footed shot from just outside the penalty area that goes harmlessly over the target.77:29
Assist on the goal came from Tim Cahill.77:29 Goal scored
Goal! - Apostolos Vellios - Bolton 0 - 2 Everton Goal scored by Apostolos Vellios from inside the six-yard box low into the middle of the goal. Bolton 0-2 Everton.75:08
Apostolos Vellios takes a shot. Save by Jussi Jaaskelainen.73:41 Substitution
Substitution Apostolos Vellios on for Louis Saha.73:41
Gretar Rafn Steinsson is ruled offside. Indirect free kick taken by Tim Howard.73:18
Leon Osman takes a shot. Jussi Jaaskelainen makes a save.70:16 Substitution
Substitution Kevin Davies leaves the field to be replaced by Tuncay Sanli.
Substitution Gretar Rafn Steinsson on for Nigel Reo-Coker.69:31
Tim Cahill takes a shot. Save by Jussi Jaaskelainen.67:48
Paul Robinson challenges Seamus Coleman unfairly and gives away a free kick. Free kick taken by Tony Hibbert.64:10
Ivan Klasnic takes a shot. Tim Howard makes a save.63:23
Leighton Baines conjures a left-footed shot from inside the six-yard box that clears the bar.62:17
Inswinging corner taken by Leighton Baines.60:54 Substitution
Substitution Darren Pratley comes on in place of Fabrice Muamba.60:18
Corner taken by Chris Eagles, clearance made by Tim Cahill.60:00
Inswinging corner taken right-footed by Chris Eagles from the left by-line, clearance by Phil Jagielka.59:37
Ivan Klasnic takes a shot. Phil Jagielka manages to make a clearance.58:35 Booking
Booking Nigel Reo-Coker is booked.57:15
Louis Saha takes a shot. Save made by Jussi Jaaskelainen.55:36
Seamus Coleman takes a shot. Jussi Jaaskelainen makes a save.55:04
Zat Knight concedes a free kick for a foul on Leon Osman. Indirect free kick taken by Marouane Fellaini.54:15
The ball is swung over by Leighton Baines.54:01
Louis Saha takes a shot. Zat Knight gets a block in.52:25
Tim Cahill handles the ball and concedes a free kick. Jussi Jaaskelainen restarts play with the free kick.50:56
Free kick awarded for a foul by Fabrice Muamba on Leon Osman. Johnny Heitinga takes the indirect free kick.48:26
Assist on the goal came from Diniyar Bilyaletdinov.48:26 Goal scored
Goal! - Marouane Fellaini - Bolton 0 - 1 Everton Marouane Fellaini scores a goal from close in high into the middle of the goal. Bolton 0-1 Everton.45:01
The referee gets the second half underway.45:00 +2:26 Half time
Half Time The ref blows to end the first period.45:00 +1:15
Foul by Louis Saha on Jussi Jaaskelainen, free kick awarded. Free kick taken by Jussi Jaaskelainen.43:19
Indirect free kick taken by Gary Cahill.43:19 Booking
Booking Leon Osman is shown a yellow card for unsporting behaviour.43:10
Leon Osman concedes a free kick for a foul on Mark Davies.42:39
Tim Cahill takes a shot. Paul Robinson gets a block in.41:02
Foul by Seamus Coleman on Paul Robinson, free kick awarded. Indirect free kick taken by Zat Knight.37:22
Free kick awarded for a foul by Johnny Heitinga on Mark Davies. Strike on goal comes in from Chris Eagles from the free kick, blocked by Seamus Coleman.36:59
Johnny Heitinga takes a shot. Jussi Jaaskelainen makes a save.35:51
Unfair challenge on Leighton Baines by Kevin Davies results in a free kick. Leon Osman takes the free kick.35:01
The referee blows for offside against Ivan Klasnic. Johnny Heitinga restarts play with the free kick.33:56
The referee blows for offside. Jussi Jaaskelainen restarts play with the free kick.32:35
Johnny Heitinga fouled by Ivan Klasnic, the ref awards a free kick. Indirect free kick taken by Phil Jagielka.30:44
Free kick awarded for a foul by Marouane Fellaini on Mark Davies. Nigel Reo-Coker takes the indirect free kick.25:17
Shot from deep inside the area by Diniyar Bilyaletdinov clears the crossbar.25:00
Shot from 25 yards from Chris Eagles. Save made by Tim Howard.24:12
Unfair challenge on Ivan Klasnic by Johnny Heitinga results in a free kick. Fabrice Muamba takes the free kick.22:23
Ivan Klasnic fouled by Phil Jagielka, the ref awards a free kick. Free kick crossed right-footed by Chris Eagles from left channel.22:01
Chris Eagles takes a shot. Leon Osman gets a block in.19:17
Indirect free kick taken by Johnny Heitinga.19:17 Dismissal
Dismissal David Wheater shown a red card for serious foul play.18:41
Diniyar Bilyaletdinov fouled by David Wheater, the ref awards a free kick.12:58
Ivan Klasnic takes a shot. Save made by Tim Howard.12:05
Free kick awarded for an unfair challenge on David Wheater by Leighton Baines. Jussi Jaaskelainen takes the indirect free kick.11:16
Corner taken by Leighton Baines, Gary Cahill makes a clearance.10:47
Corner taken by Leighton Baines from the right by-line, Jussi Jaaskelainen makes a save.9:50
Outswinging corner taken left-footed by Leighton Baines from the left by-line, Tim Cahill takes a shot. Gary Cahill gets a block in.5:06
Free kick awarded for an unfair challenge on Leon Osman by Kevin Davies. Indirect free kick taken by Johnny Heitinga.3:32
Marouane Fellaini is ruled offside. Indirect free kick taken by Jussi Jaaskelainen.2:47
Foul by Paul Robinson on Seamus Coleman, free kick awarded. Leighton Baines delivers the ball from the free kick left-footed from right channel, Jussi Jaaskelainen makes a save.2:20
Seamus Coleman takes a shot. Paul Robinson gets a block in.1:11
Chris Eagles is caught offside.0:45
Effort on goal by Kevin Davies from deep inside the area goes harmlessly over the bar.0:00
The game begins.
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