Paul Scharner opened the scoring before Chris Brunt doubled the advantage with a brilliant free-kick.

Tim Cahill pulled one back but West Brom took advantage of the sending-off of Mikel Arteta to secure victory through Somen Tchoyi and a Youssouf Mulumbu effort which was deflected in by Sylvain Distin.

Di Matteo said: “There were some excellent goals today – we were very clinical, which has been missing in the last few weeks from our game.

“I thought we played some fantastic football, we didn’t show any fear.

“We showed a lot of courage to come here and play the football we did.

“We rode our luck a bit at 2-1 and our keeper made some great saves to keep us in the game.

“But the quality of our play and the quality of goals gave us our advantage.”

The only downside for the Baggies was the late sending-off of Mulumbu for two bookable offences.

The Democratic Republic of Congo international received his first yellow card for over-celebrating his goal and the second came moments later for a challenge on Steven Pienaar.

The goal and the two cards all came within the space of three minutes.

Di Matteo said: “He needs to learn a bit, but I think the second yellow card was a bit harsh. I don’t think he touched the opponent and I think he got the ball as well.

“If we have yellow cards for those challenges we should have 20 in every game.”

Di Matteo had no doubts about Arteta’s dismissal, however.

The Spaniard was challenged heavily by Gonzalo Jara and appeared to react by stamping twice on the Chile defender.

Di Matteo said: “I think Arteta stepped on Jara and it was just in front of the dugout, so everyone saw it.”

The incident occured just seconds after Jara had collided with Leighton Baines on the edge of the area, a challenge which went unpunished.

Everton boss David Moyes said: “I’m not going to talk about the sending-off, I’ll only talk about what happened prior to it.

“It was a free-kick on the edge of the box, which should have been dealt with. The referee is close enough to see it.

“It was an elbow in his face, on Leighton Baines. The player led with his elbow. As far as I am concerned that is the decision we should be talking about.”

Moyes, however, did not look for excuses for his team, who have now gone five games without a win.

He said: “We didn’t start well. We went a couple of goals down because of our poor start.

“You can play badly and maybe get away with it but we didn’t get away with it today because we didn’t pick up well enough.

“We were terrible in the first half, we got the goal and I told them (at half-time) they had 10 minutes to get another goal back and then I’d make changes. I did that.

“The players had a go and in truth we were maybe close to winning it at one point, but in the end we’ve ended up losing quite heavily.”

One of the players sent on in the second half was Jermaine Beckford, who had a shot cleared off the line and then squandered two gilt-edged chances.

“You’ve got to score,” admitted Moyes. “When chances come like that, whatever level, that’s it. It is very rarely you get as many. You have got to score.”