But the hosts, who had lost eight of their previous 13 league games at Old Trafford, started strongly against Burnley.
Mbeumo twice went close inside the first 15 minutes, before United were awarded a penalty for a foul on Mason Mount, only for VAR to overturn the decision.
The pressure paid off, however, when Casemiro's header came back off the crossbar before going in off Cullen.
Amad should have made it two in first-half stoppage time, before substitute Joshua Zirkzee, who replaced the injured Matheus Cunha, missed another golden chance.
The nerves set in after the break, as Foster was left all alone from Jacob Bruun Larsen’s cross to level, only for Diogo Dalot to pick out new signing Mbeumo who netted his first league goal for United.
Bayindir, at fault for Arsenal's winner on the opening day of the campaign, then failed to deal with another set piece, parrying the ball out to Anthony who made no mistake from close range.