The experienced striker stooped to head home in the final 10 minutes of the match to give his side the upper hand ahead of the second leg at Vicarage Road on Sunday
The match had been a cagey affair throughout but Nugent's late intervention, an unorthodox header from Anthony Knockaert's inviting free kick, gives the Foxes real hope of causing an upset at the Hornets' Vicarage Road home and securing a trip to Wembley.
The first half saw Ickechi Anya and Almen Abdi have low shots well saved by Kasper Schmeichel before the outstanding Knockaert tricked his way back from the byline before his stinging drive was turned aside at the near post by Manuel Almunia.
Watford continued to enjoy the better chances and should have grabbed a crucial opener when the ball bobbled through the hosts' defence to the deadly Matej Vydra midway through the second half, but the out-of-form Czech Republic international tamely rolled the ball into the hands of Schmeichel.
Alexandro Geijo also wasted a gilt-edged opportunity as he mistimed his far-post header after out-jumping Ritchie De Laet as Watford desperately sought a breakthrough but they were undone against the run of play as Nugent, without a goal in 16 games, found the perfect time to stop the rot and put the Foxes firmly en route to the final at the half-way stage of the tie.