Aaron Wilbraham capped a man-of-the-match performance with the opener in this second round clash, before Wade Small's tap-in and Gary Smith's cool finish two minutes from the end sealed the Dons' fourth straight win at a foggy Underhill.
Dons boss Danny Wilson made a host of changes to the line-up that beat Walsall 2-1 on Saturday, with most notably Nathan Koo-Boothe handed his first start of the season at centre-half as a number of regular first-teamers were given a rest.
The Dons had total control of the early stages as Barnet struggled to get out of their own half and, after Gareth Edds skewed Malvin Kamara's pull-back wide from the edge of the box, Wilbraham put them ahead in the 10th minute.
Nicky Rizzo whipped an excellent in-swinging free-kick into the box from the right and Wilbraham rose unchallenged to glance home his second goal in two games from seven yards.
Rizzo's fierce angled drive was palmed away at full-stretch by Bees' goalkeeper Scott Tynan in the 21st minute as the visitors continued to dominate, before Dons' keeper David Martin was forced to make a magnificent save at the other end to keep out Jason Norville's header.
Dwane Lee lofted a free-kick into the box and the unmarked Norville's powerful close range header was tipped out of the top corner by Martin in the 38th minute.
And just a minute later Small rubbed salt into the hosts' wounds by putting the Dons 2-0 up.
Rizzo raced clear onto Koo-Boothe's ball down the left and unselfishly played it across goal for Small to tap home unmarked from six yards.
Small had another good chance well saved by Tynan on the stroke of half-time, before Wilbraham was denied his second of the match just a minute after the re-start when he broke clear only to see his attempted lob blocked by the Bees' keeper.
But Paul Fairclough's men battled back and Anthony Charles smashed Nicky Bailey's pull-back just over the bar from the edge of the box, before Martin had to be alert to tip Bailey's 30-yard curler around the post in the 68th minute.
At the other end, Smith latched onto Small's through ball but his strike from an angle was saved by Tynan's legs, before he made no mistake in the 88th minute.by putting the Dons 3-0 up.
Substitute Stephen Quinn collected Wilbraham's pass before laying a clever ball inside to the unmarked Smith, who calmly slotted the ball past Tynan to seal the rout.

Barnet: Tynan 7, Batt 5 (Devera 89, 6), Yakubu 6, King 7, Charles 6, Bailey 7, Strevens 5 (Soares 71, 6), Lee 6, Bowditch 5, Roache 4 (Hatch 78, 6), Norville 6. Subs: Flitney, Hatch, Hickie, Devera, Soares.

MK Dons: Martin, Lewington, Small (Quinn 78), Smith, Edds, Kamara (McKoy 57), Rizzo (Puncheon 89), Koo-Boothe, Crooks, Wilbraham, Mills. Subs: Platt, Oyedele, Puncheon, McKoy, Quinn.

Referee: Mr I Williamson.

Attendance: 991.