Second-placed Albion were off key in the opening period but were a different proposition in second half.
Own goal: Peterborough's Ryan Bennett heads into his own net under pressure from Graham Dorrans
Luke Moore, who had scored twice against Peterborough in Albion's 3-2 win at London Road in August, broke the deadlock with his fourth goal of the season in the 61st minute.
Peterborough's Ryan Bennett then headed into his own net eight minutes later as Albion earned their first win in four games.
Albion are now two points clear of third-placed Nottingham Forest and have cut the advantage of leaders Newcastle United to eight.
Di Matteo said: "I told the players to stay patient because it is important to stick to your game plan.
"But I also had to raise my voice a little bit because I disagreed with how we played in the first half. When it is needed I can do that.
"We were slow in the first half and there wasn't much movement. It just didn't happen for us in the first half. We didn't penetrate the Peterborough defence enough.
"We did increase the tempo in the second half and managed to score two goals and I think we deserved to win.
"When you win it is always a good day and, as you can see from the other results, it is difficult to win a game in this league.
"If we can now beat Scunthorpe on Monday we can end the first half of the season with a nice cushion of points."
Peterborough manager Mark Cooper had seen the team win their first game under his control in their previous match against Watford.
They held out for an hour against Albion but are now four points from safety and Cooper said: "We just caved in which is the disappointing thing for me.
"We were pretty comfortable for an hour.But it is becoming a bit of a trait now that when we come under a bit of pressure we concede, not just one, but two very quickly.
"It is something that needs addressing. We gifted West Brom two goals.
"For the first goal we let Graham Dorrans skip through three challenges which isn't good enough.You have to get tight to people and deal with it better than that.
"We have to stand up, roll our sleeves up and see it through until the pressure comes to an end."
Cooper has hinted he will move into the transfer market to try to solve his side's difficulties and he added: "I am sure that if we find the right players there will be money to spend.
"We need a right-back and we probably need another forward and a midfield player."
Albion made the decisive breakthrough when Dorrans surged forward from midfield to set up Moore who drilled a low drive past Joe Lewis from eight yards.
Bennett then sealed Albion's success by heading the ball into his own net under pressure from Dorrans following a shot by Moore.
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Source: Daily_Mail
