Having beaten Wolves 2-1 at home last weekend, the Toffees moved out of the bottom half up to eighth in the table with this afternoon's result.

Prior to those matches Moyes' side had lost five out of six league fixtures, and the Scot is optimistic that they are now "picking up" as they have done in previous campaigns.

"We have been slow starters in the past, although I didn't actually think we had started slow this year," Moyes said.

"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.

"I'm hoping that this could be the start of us moving forward."

Everton took the lead four minutes after the break when Marouane Fellaini swept in from close range, before substitute Apostolos Vellios netted a second 12 minutes from time.

Bolton had earlier had David Wheater sent off, the defender being shown a straight red card in the 20th minute for a lunge on Diniyar Bilyaletdinov after losing control of the ball, his second dismissal of the campaign.

Asked if he thought referee Michael Oliver had made the right decision regarding Wheater, Moyes said: "I did at the time and I was right in front of it.

"I don't think David Wheater is by any means that type of player, but his touch just overruns the ball and he definitely catches Bilyaletdinov.

"I'm standing five or six yards away from it and it was the correct decision. If it had been one of my players, I would have expected a red card."

Bolton boss Owen Coyle - whose side suffered their 10th league defeat this term and remained in the relegation zone - said he was not surprised to see Wheater dismissed given the nature of the challenge.

"David took a bad touch, there is no getting away from that, and he tried to recover it," Coyle said.

"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.

"In my day and age it probably would have been a yellow card, because I think he would have recognised that he took a bad touch - he hadn't come flying in from 40 yards trying to hurt the lad.

"To his credit, Bilyaletdinov was snap on to it (when Wheater lost the ball) and those are the rules. I can't say it surprised me."

Meanwhile, Moyes revealed that Toffees midfielder Jack Rodwell could soon be back in training as he continues his recovery from the rib injury - sustained on international duty with England - which has kept him out of his club's last two matches.

"He has been for another scan this morning and it is showing that he is getting better," Moyes said.

"I'm expecting him to maybe be back in training by the middle of next week, everything going well."