United conceded early goals in both halves at Brunton Park and fell to defeat despite a consolation goal from Matty Dennis.
Mark Hughes made four changes from Saturday's defeat at Harrogate, with Jordan Jones, Josh Vela, Matty Dennis and Joe Bevan coming into the starting line-up.
The visitors took the lead with less than two minutes on the clock when a loose ball fell kindly on the edge of the box. Smith got it to Maycock who finished well into the top corner.
Smith was involved again for the away side with 18 minutes on the clock. His shot was spilled by Breeze but Bugiel's shot from the follow up went over the bar.
Stevens was the next Dons' player to take a shot on after he turned quickly on the edge of the box, but it lacked power and Breeze claimed it.
United started to gain some momentum with Jones and Bevan having crosses from either side of the box cleared. Davies then got a dangerous ball into the box, Dennis' flick was blocked, as was his follow up shot, then Harris sliced his effort wide under pressure.
Davies was involved again just before the break, he cut inside and took a shot on with his left foot but it went over the bar.
Callum Guy had the last effort of the half with a shot from 25 yards, but the keeper watched it all the way.
HALF-TIME: United 0-1 AFC Wimbledon
The visitors doubled their lead with 49 minutes on the clock. Neufville recycled the ball in the box and got a cross in which Smith finished well past Breeze.
United created the next opportunity after an hour when Kadeem Harris made progress on the right. He got a good cross in but Harper's header was deflected behind for a corner.
Matty Dennis got a goal back for the Blues with 67 minutes played, Harris got the cross in from the right again and Dennis made no mistake with his head at the back stick.
Hippolyte controlled a ball into the box for the Dons with 75 minutes on the clock but his shot went wide of Breeze's post.
Long throws from Cedwyn Scott put Wimbledon on the backfoot and a cross from Sam Lavelle was headed behind for a United corner. Owen Goodman in the visitors' goal claimed the resultant set piece.
Late pressure from United didn't result in a clear-cut chance and the visitors went home with the three points.
FULL-TIME: United 1-2 AFC Wimbledon
Teams:
United: Breeze, Davies, Harper, Thomas, Lavelle (C), Guy (Whelan 66), Jones (Embleton 85), Vela (Wearne 66), Dennis (Kelly 85), Bevan (Scott 54), Harris.
Unused subs: Lewis, Hayden.
AFC Wimbledon: Goodman, Furlong (Ogundere 65), Reeves (C), Johnson, Maycock (Hippolyte 66), Bugiel, Neufville, Smith, Stevens (Kelly 79), Lewis, Hutchinson.
Unused subs: Ward, Browne, Harbottle, Sasu.
Goals:
United - Dennis (67),
AFC Wimbledon - Maycock (2), Smith (49)
Yellow cards:
United - Lavelle (92)
AFC Wimbledon - Furlong (15), Hutchinson (87)
Red cards:
United - N/A
AFC Wimbledon - N/A
Match officials:
Referee - Martin Woods
Assistant Referee 1 - Daniel Woodward
Assistant Referee 2 - Emily Carney
Fourth Official - Conor Brown
Attendance: 7,050 (511)
