After falling to eighth after losing 1-0 to Stoke at the weekend, United went back up to fifth after Ollie Norwood’s ninth-minute strike secured victory by the same scoreline at Bramall Lane.
With just six games left of the Championship campaign, United are two points adrift of third-placed Huddersfield Town but only two clear of Blackburn in seventh.
"Any win when you're playing someone around you is big, of course it is,” Heckingbottom admitted.
“It gets even bigger at this business end of the season and with what's at stake. It's a big win, a good win. I was pleased with lots of things I saw.
"I thought we played well and were good value for the 1-0. We got in some really good positions as the game wore on and started the second half well.
"Probably the only criticism was that we didn't create enough chances off the back of the good play we were having and when we were winning the ball high.
"While ever that happens, and there’s only one goal in it, you know at some point you know you're going to have to weather a storm. Teams are going to take chances, they're going to put bodies higher up the pitch, play forward more.
"If we'd capitalised with one of the breaks we had, for instance when Morgan [Gibbs-White] went through, things would have been lot simpler.
“But the fact it wasn't meant we had to rely on that defensive solidity.”