Brighton had been the better team up until Young's attempt from the edge of the area hit Lewis Dunk before looping over keeper Mat Ryan and into the net.
Earlier, Anthony Knockaert and Pascal Gross both went close after getting behind the United defence.
Ryan produced a double save to keep out Romelu Lukaku's header and Paul Pogba's follow-up on the stroke of half-time.
United's win cuts Manchester City's lead at the top of the Premier League table to five points ahead of their trip to Huddersfield on Sunday.
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