United took a two-goal lead into half-time thanks to Fernandes’ penalty and Greenwood’s powerful drive.
Villa had been on top before the visitors’ opener, which came from a controversially-awarded penalty given for Konsa’s supposed challenge on Fernandes.
There was nothing controversial about the second as Greenwood drilled the ball in from range after Martial turned over possession inside his own half.
58 minutes on, Pogba wraps up the three points for United. Fernandes picked out the unmarked Pogba from the corner and the Frenchman, after initially struggling to get the ball out of his feet, sends a 20-yard shot spinning away from Reina.
While United remains in fifth, the porous Villa remain 19th and in huge trouble.
The Red Devils are now 17 matches without defeat in all competitions.