Bamford opened the scoring with a flicked header from six yards after being picked out by Shaun Williams' delivery from the left wing.
The 19-year-old striker, on-loan from Chelsea, rose above early substitute Max Ehmer to head the ball into the top left corner.
Lowe, who had only been on the pitch for 10 minutes, then wrapped up the win in the 77th minute when he slotted the ball into the bottom corner. The Dons midfielder tackled Mark Roberts on the edge of the area before taking the ball around Chris Day to leave himself with an open goal.
Stephen Gleeson denied Stevenage a first goal in five games by clearing James Dunne's goalbound 60th-minute corner off the line after Boro had wasted two good opportunities to equalise before the break.
Matt Ball saw a tame effort saved by a scrambling Ian McLoughlin after Marcus Haber had dispossessed the MK Dons 'keeper and passed the ball across the box.
Roberts had a shot saved from close range two minutes before half-time after being found unmarked from Dunne's free-kick.