United got off to the perfect start, scoring in the first five minutes when debutant defender Rob Gould rose highest to nod home Drew Roberts' raking free-kick. 1-0 Aylesbury
After Scott McCafferty fired wide, the Ducks suffered a blow as centre-back Kamran Abassi was forced off with an injury to be replaced by Liam Folds.
Unsurprisingly Aylesbury put their 'hosts' under plenty of pressure, but so often throughout the match were unable to finish their chances. Jaggard dribbled into the box but wasted his hard work by blazing over, and McCafferty saw a shot deflected wide after a great passing move.
Folds of all people played a fantastic pass to pick out Roberts, goalkeeper Paul Searl was out smartly and saved his effort well. Searl foiled Roberts again five minutes later, tipping his viciously dipping free-kick over the bar.
From the resultant corner the away side finally doubled their lead. The ball ricocheted about dangerously in the box, and as players madly swiped the ball bounced around in pinball style, before Edgeworth managed to prod home. 2-0 Aylesbury
Aylesbury's third right on half time was a little more tidy, Gould rising to nod home from a corner kick, his second goal of his debut. 3-0 Aylesbury
Half-time: Thame 0-3 Aylesbury
Thame made two changes at half-time in an effort to improve their fortunes, and substitute Paul Mitchell had the first chance after the restart, his curling effort easily gathered by Rashid. Searl held a McCafferty free-kick at the other end.
Jack Rashid hadn't had a lot to do in the game, but he was called upon after 56 minutes to make a miraculous one-handed save from a goalbound header from a corner kick. Moments later Mitchell headed a cross over when he really should have hit the target.
Any fears of a Thame resurgence were finally laid to rest just past the hour mark. Gavin Jaggard took advantage of a calamitous mistake by a Thame defender 5-yards from goal to bury the ball home, after Roberts' fine run and low cross from the left. 4-0 Aylesbury
Just two minutes passed before the Ducks added another, at this point threatening to run up a big scoreline. Jamie Kearns' shot from the edge of the area was spilled by Searl, and Neil Lazarus followed up to score his first goal for the club. 5-0 Aylesbury
The remainder of the game saw an amazing number of chances come and go for the Ducks, with the score somehow being limited to five by a combination of excellent goalkeeping and some poor finishing.
Edgeworth had a header well saved from Roberts' cross, and Dean Powles missed a close range volley having been brilliantly picked out by substitute Daniel Mead.
Thame went close through Wayne Spencer, their final effort of the game. As space opened up for the substitute he dragged his shot wide of Rashid's post.
Normal service was soon resumed and the chances began to fall again. Jaggard held the ball up well, and fed Kearns who unfortunately miscued his shot well over. Jaggard then played the ball to Roberts, who also fired off target.
Searl made a good double save to deny first Roberts when clean through, before recovering well to tip Kearns' goalbound effort onto the bar, despite being well off his line.
This was to mark the end of Aylesbury's goal attempts, the final action of the half seeing Spencer shown two yellow cards in the space of two minutes for dissent.
Aylesbury's reward for the win is a trip to Halesowen Town or Willenhall Town in the next round.