A Richard Cresswell hat-trick set up a tie against The Toffees at Goodison Park later this month.
Cresswell put the Whites ahead but the home side hit back with two goals, the first a Joey Gudjohnsson penalty after defender Claude Davis was shown a red card for a foul on Gareth Williams.
Nathan Blake bagged the second Foxes goal but Cresswell grabbed a last minute equaliser for the Whites from the penalty spot and 7 minutes from the end of the extra time period his third goal of the night set up a mouth-watering tie against Premiership opposition later this month.