United trailed 2-0 on the south coast when Cavani was brought on at half time.
The forward assisted Bruno Fernandes for United’s first goal before two late headers of his own sealed a tremendous 3-2 win for Ole Gunnar Solskjaer’s side.
The victory made it four wins in a row for the Red Devils in all competitions and eight straight away Premier League wins.
Cavani joined United on a free transfer on deadline day in the summer following his release from PSG at the end of last season.