Pogba doubled United's lead minutes later after Jesse Lingard drove at Palace's defence before playing a square pass that the Frenchman slotted home after a slip by Joel Ward.
Christian Benteke headed against the post after the interval as Palace ended the season in 14th place. United, who face Ajax Amsterdam in the Europa League final on Wednesday, finished sixth.
(Reporting by Simon Jennings in Bengaluru; Editing by Toby Davis)
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