The Red Devils have won their last three games in all competitions to help ease the pressure on Manchester United manager Jose Mourinho.
Manchester United lost successive Premier League games after defeats by Brighton and Hove Albion and Tottenham Hotspur earlier this term.
The 20-time English champions bounced back with victories either side of the international break after notching up wins against Burnley and Watford.
Paul Pogba scored twice in Switzerland on Wednesday night to help Manchester United ease to a 3-0 win over Young Boys in their Champions League opener.
Wolves have made a positive start to the season after collecting seven points from their opening five Premier League fixtures.
Indeed, the promoted side are the only Premier League club to stop Manchester City so far after a goalless draw with the defending champions.
Former Liverpool FC defender Lawrenson believes the Red Devils will edge to narrow win over Wolves at Old Trafford on Saturday.
“All sorts of questions were being asked about Manchester United when they lost to Tottenham at the end of August, but since then they have won three out of three, all away from home,” Lawrenson told BBC Sport.
“I have been impressed by Wolves, but I thought Burnley would go to Molineux last week and pinch the points.
“I was wrong – and Nuno Espirito Santo’s side played really well. The way they play, and with the amount of possession they enjoy, they are going to create lots of chances against teams – and they have got better defensively too.
“But United have got some momentum now and their troubles seem a long time ago. I can only see a home win.”
Manchester United signed Shakthar Donetsk midfielder Fred, FC Porto defender Diogo Dalot and Stoke City goalkeeper Lee Grant in the summer transfer window.
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