It was no more than the Boro deserved after a much-improved display in the second half and there was a very encouraging performance by last week's signing Francois Zoko, who struck on his debut.
Shaun Williams came close to giving MK Dons an early lead when his free kick was superbly tipped on to the crossbar by Stevenage goalkeeper Chris Day.
But the Dons' centre-back was successful from the penalty spot in the 26th minute by sending Day the wrong way after Luke Freeman bundled over Izale McLeod in the area.
Stevenage drew level five minutes into the second half when Michael Doughty's cross allowed Zoko to finish comfortably from close range.
The Ivorian striker was then involved in the penalty that won the Boro the match when he was sent tumbling by Williams, with Felipe Morais coolly rolling the spot kick into the bottom corner.