It was looking as though the hosts were going to be frustrated by Steven Schumacher's first-half penalty miss, but two goals in the final eight minutes from Craig Jones and Johnson Clarke-Harris earned Bury only a fourth home win all season and just a seventh in total in League One.
Standing in for manager Kevin Blackwell, Futcher, whose side went into the game on the back of a dismal run of six defeats in their previous seven, said: "The lads were outstanding and I can't praise them highly enough."
He continued: "We knew this was going to be a tough game. That's exactly how it panned out, but we've got a great spirit in the camp and it came to the fore perfectly late on. The main job is to put the ball in the back of the net though, and thankfully it's worked out for us.
"We just have to keep going. We have to keep creating the chances, and if we do that, we'll pick up the points we need. It was definitely a deserved win, but I guess it has to be about building on this momentum as much as we can now.
"We're off the bottom, and of course the lads still believe they can get out of the bottom four."
Stevenage boss Gary Smith was clearly disappointed after his stuttering side slid to a ninth defeat from their last 11 games. Smith said: "That just highlights, once again, our Jekyll and Hyde performances of late.
"We were overjoyed on Saturday after the win against Sheffield United, but that showing bore no resemblance whatsoever to the weekend. That's been the challenge throughout really, to find that consistency.
"We have to compete better, much better. Going forward we looked toothless, we lacked ideas far too often. We looked as unreliable as I have seen us for a very long time.
"It's been a tough night for us all. We've made the long journey up here and we'll be going back home with nothing."