First half strikes from Jeremiah Gyebi and Samyan Ismail put the young Glovers on their way before Reuben Collins grabbed a goal back for the visitors late on.
Nestor Sako restored the two-goal advantage in the closing stages to ensure Town’s progression.
In a quiet start to proceedings, neither keeper was forced into action in the opening 25 minutes as both sides enjoyed spells of possession.
However, just past the half-hour mark the deadlock was broken through a well-worked Yeovil free-kick.
Jack Rice-Lethaby’s short pass teed up Gabriel Rogers, whose driven effort was turned into the back of the net by Gyebi who capitalised on a static Dons defence.
The hosts’ lead was soon doubled after the award of a penalty on 39 minutes.
Nzembela’s strong run was brought to an end inside the box, allowing captain Ismail to step up and send the goalkeeper the wrong way from 12 yards.
Causing havoc before the break, Nzembela forced a good save with an acrobatic shot from inside the penalty area as Wimbledon held on to keep the score 2-0 at half-time.
After a disappointing opening 45 minutes the visitors offered more of a threat after the restart as Judah Chapman’s venemous strike had to be parried away by the diving Tommy Scott.
Having enjoyed a spell of pressure, the Dons grabbed a goal back with a little over 10 minutes remaining when Tyler Burey’s wide free kick was turned in by Collins.
With a comeback on the cards, Town sealed their place in the next round when Paulius Golubickas picked out Sako with a perfectly weighted through ball, which the Yeovil striker confidently slotted into the net to seal victory.