The Arsenal loanee, who also scored twice in the Dons’ 4-0 rout of Manchester United in the previous round, took his tally in the competition to an impressive five goals in three games.
It took MK Dons just five minutes to go in front when Darren Potter played in Afobe, who turned before powering his shot across goal and into the bottom corner.
Bradford’s best chance came when Billy Clarke picked out Mason Bennett on the right with the 18-year-old cutting inside before bending his effort just wide.
The Dons came within a whisker of a second goal when Kyle McFadzean’s low drive from 25 yards came back off a post, but Afobe sealed the tie with five minutes left.
Sent clear by a long ball over the middle, he was through one-on-one and confidently slid the ball past Bradford goalkeeper Ben Williams.