The Red Devils have won their last four games in all competitions to relieve pressure on manager Louis van Gaal over his long-term future.
United boss Louis van Gaal is overcoming every hurdle placed in front of him at the moment
The 20-time English champions have beaten Shrewsbury Town, FC Midtjylland, Arsenal and Watford in their last four games.
West Brom, meanwhile, have beaten Crystal Palace and draw with leaders Leicester City in their last two Premier League games.
Former Republic of Ireland defender Lawrenson believes the Baggies can get a result against Van Gaal’s improving Red Devils side on Sunday afternoon.
“Manchester United’s good run continued with their win over Watford and they are now level on points with fourth-placed Manchester City, although they have played a game more,” Lawrenson told BBC Sport.
“United boss Louis van Gaal is overcoming every hurdle placed in front of him at the moment but in the long term I don’t think it will change people’s opinion on him or whether he stays in his position.
“West Brom have had a good few days, taking four points from Crystal Palace and Leicester, and that has ended any lingering doubts that they might get dragged into the relegation scrap.
“Baggies boss Tony Pulis will make plans to stop United, and I think they will work.”
United moved level on points with fourth-placed Manchester City on Wednesday night thanks to their 1-0 win against Watford.
Juan Mata scored the home side’s winner in the 83rd minute at Old Trafford to maintain their winning run.
United make the trip to Liverpool for the first leg of their Europa League last-16 tie on Thursday night.
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