Keston Davies’ first professional goal gave the Glovers a merited lead on 48 minutes and Jake Gray completed the scoring late on with his first Yeovil strike.
The victory was the home side’s third against a Sky Bet League One outfit this term, and ensured their name went into the hat for Friday’s draw.
Saturday’s last-gasp goal hero Jordan Green was granted his fourth start of the season as Darren Way made five changes from the Emirates FA Cup draw at Port Vale.
Davies renewed his centre-back partnership with Omar Sowunmi which proved effective in this competition against Plymouth Argyle a week ago, while Tom James switched to left-back to accommodate Bevis Mugabi on the other flank of defence.
Elsewhere, Oscar Gobern, who made his Glovers debut at Vale Park, and Connor Smith coupled up in central midfield, and it was the duo who combined for the game’s opening shot.
Captain Gobern’s slide-rule pass cut open the Wimbledon backline and Smith fired over with his left foot on the angle after two minutes.
Otis Khan then warmed the gloves of Joe McDonnell with a cheeky dinked attempt as Town set their sights on an early goal.
They couldn’t quite find it but remained calm, pressed when they needed to and passed the ball around with precision, leading to Sam Surridge nodding high into the away terrace.
Moments later the AFC Bournemouth youngster went down in the area over the sitting George Francomb following a swift counter-attack, created by a determined Gobern and pacey Green. Nothing given.
The latter used his speed again to this time skip past Will Nightingale to the byeline, cut inside to have a go but his shot lacked conviction to trouble McDonnell.
Town goalkeeper Artur Krysiak was finally called into action just past the half-hour mark, getting low to hold on to a tame Francomb strike before a piece of brilliance from Sowunmi almost resulted in a Yeovil goal.
The giant centre-back spread a 40-yard crossfield ball to Khan; he skipped down the left and delivered for Surridge whose header was cleared from underneath the crossbar by Dons skipper Paul Robinson.
Yeovil’s dominance was frightening and they deserved a lead to take into the break, however McDonnell had other ideas.
Versatile Welshman James has gained a reputation for his knuckleball free kicks and his latest attempt looked to be heading for the top corner, but for a fantastic flying stop from the Wombles stopper.
Although their first-half endeavour went unrewarded, the hosts went ahead minutes into the second period.
Khan’s corner to the front post was flicked goalward by Davies, the post prevented the ball rustling the net but assistant referee Justin Amey stuck his flag in the air to alert man in the middle Antony Coggins that it had crossed the line.
Despite their continued attacking intent and willingness to commit bodies forward, Yeovil didn’t test McDonnell thereafter with James hitting another set piece wide and substitute Francois Zoko smashing a venomous shot against the face of young defender Toby Sibbick.
The Green and Whites did grab another goal, and justifiably so, when Gray, fresh off the bench, sent a low drive into the corner to confirm a place in round three of the Checkatrade Trophy for the second consecutive campaign.
Yeovil Town: Krysiak, Mugabi, Sowunmi, Davies, James, Green (Gray 82), Gobern (Worthington 74), C.Smith, Khan, Olomola, Surridge (Zoko 70).
Bookings: None.
Not Used: Maddison, N.Smith, Bailey, Santos.
AFC Wimbledon: McDonnell, Sibbick, Robinson, Kalambayi, Nightingale, Kennedy (Ashley 80), Francomb, Abdou, McDonald (Evans 60), Forrester (Nelson-Roberts 60), Kaja.
Bookings: Kalambayi 25, Abdou 61
Not Used: Tzanev, Urhoghide.
