United took the lead after only eight minutes when Steve Callinan fired home inside the box following Darren Grieves' header down into his path.
However, Lewes came back at the Ducks and scored an equaliser a couple of minutes later when a weak shot in the area rebounded off Scott Honeyball's legs and into the net.
Just after the half-hour Aylesbury re-took the lead when Callinan converted from the penalty spot after Highton was brought down. It almost became 3-1 on the stroke of half-time but Grieves was unlucky to see his shot come back off the crossbar.
In the second half Lewes fought back strongly and aided by a lack of concentration in the Aylesbury defence carved out a few good chances but were unable to beat Courtnage. With five minutes to go Roni Joe had a good chance to wrap the game up, but unfortunately strayed offside when the ball was played to him by the clean-through Peter Donnelly. However, this didn't matter as Aylesbury held on for the win and went on to play Ware in the next round.