After a goalless first half, Robin Shroot edged Boro ahead in the 55th minute before a quick-fire double turned the contest on its head.
Hope Akpan slotted home on the rebound after 65 minutes before Bulman's deflected strike four minutes later left Stevenage with just one win in six games.
In Stevenage's first home game since the death of their former player Mitchell Cole, both sides held a moments silence while the Boro players warmed-up in shirts carrying the number 21.
The deadlock was broken when Shroot collected David Gray's centre to slot his seventh goal of the season past Paul Jones.
The lead was to last just 10 minutes, as Steve Arnold got down smartly to repel Nicky Adams' firm drive, only for Akpan to tuck home the rebound.
And the turnaround was complete four minutes later, courtesy of Dannie Bulman's long-range strike, which flew past Arnold via the head of the unfortunate Bondz N'Gala.