A brace from Benik Afobe saw the Dons progress to the last 16 of the Capital One Cup for the first time in the Club’s history.
Robinson made three changes for the battle with the Bantams with Jordan Spence, Samir Carruthers and Afobe replacing George Baldock, Daniel Powell and Will Grigg.
Like in Saturday’s 6-1 win over Crewe Alexandra, the Dons got off to a flying start when Afobe received a pass from Darren Potter, turned magnificently away from his marker and fired an unstoppable 20-yard shot into the bottom left-hand corner. Five minutes on the clock, 1-0 Dons and already the Arsenal loanee’s eight goal of the season.
The visitors responded through Billy Clarke, who forced David Martin into a save away to his right, but that was a rare foray forward for Phil Parkinson’s men in an opening quarter controlled by the Dons.
A sensational back-heel from Carruthers created another chance for the Dons on 18 minutes, with Ben Reeves ultimately seeing a shot deflected into the arms of Ben Williams from the edge of the area after being found by Afobe.
Reeves curled a long-range free-kick over the top shortly afterwards while, at the other end, Kyle McFadzean was in the right place at the right time to head away former Don Filipe Morais’ right-wing cross.
A lull in action followed which allowed Phil Parkinson’s men to get a stranglehold in the game, and Mason Bennett curled an effort wide of the target just past the half-hour mark.
However, the men from MK1 are always threatening going forward and Dean Bowditch volleyed Reeves’ delivery over the top, before referee Mick Russell waved away strong penalty appeals when Carruthers appeared to be brought down five minutes before the break.
Alli saw a speculative effort deflected just wide as the Dons ended the first half the stronger of the two teams, which they continued at the start of the second period with Spence sending an effort just past the post following excellent work by Bowditch.
Afobe almost had a second on 56 minutes but his shot from an acute angle was blocked by the legs of Williams after being found inside the Bantams’ box.
The Dons came even closer to opening up a two-goal advantage just past the hour mark when McFadzean’s thunderous shot came back off the post. Reeves fired the rebound inches wide of the top right-hand corner.
Bradford then enjoyed a spell of pressure as they went in search of an equaliser but they failed to register a further shot on target until the 80th minute when Martin gathered Jason Kennedy’s effort from 12 yards out.
Reeves tried to settle matters with just six minutes remaining but, after some nice footwork to get away from two Bradford defenders, he flashed his effort well wide.
Not to worry, Afobe wrapped up the tie in clinical fashion on 86 minutes, latching on to Alli’s pinpoint through-ball and coolly finishing past Williams from 12 yards.
The result sees the Dons in the hat for the fourth round of the League Cup for the first time, with the draw set to take place following the conclusion of Wednesday’s fixtures.
Starting XI: Martin; Spence, Lewington, Kay, McFadzean; Potter, Alli; Carruthers (Grigg 78), Reeves (Baldock 90+1), Bowditch (Powell); Afobe.
Unused subs: McLoughlin, Flanagan, Randall, Hitchcock.
Goals: Afobe 6, 86
Bookings: Bowditch, Carruthers.
Attendance: 5,707 (572 away)