Zlatan Ibrahimovic came off the bench to sink Blackburn after Marcus Rashford equalised in the first half following Danny Graham’s opener.
It was second from bottom of Championship hosting the revitalised FA Cup holders on Sunday with a place in the next round of the cup at stake.
Danny Graham sent the home fans into delirium with a well taken opener in the 17th minute but 10 minutes later Henrikh Mkhitaryan sent Marcus Rashford clean through and the England international made no mistake as he poked home after rounding the goalkeeper.
As the rain beckoned down at Ewood Park, Jose Mourinho turned to Paul Pogba and Zlatan Ibrahimovic for inspiration in the second 45 and it was a tactical masterclass.
The Swede notched up his 23rd goal in the 75th minute in what proved to be the winner as United kept their good run of form going despite more than a few moments of anxiety as Rovers punched above their weight.
Mourinho’s attention now turns to the return Europa League clash at Saint Etienne before Sunday’s EFL Cup final against Southampton.