Nugent rose high to head in a left wing free-kick with eight minutes to go to give Nigel Pearson's team a slender advantage to take into the return fixture at Watford on Sunday.
Crystal Palace host Brighton and Hove Albion in their first leg on Friday.
The winners go through to the play-off final at Wembley on May 27, a match that will decide who joins champions Cardiff City and second-placed Hull City in winning promotion to the Premier League.
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