The promotion-chasing Blades were far from their best in the first half against Heckingbottom’s boyhood club, who are in relegation trouble but were on top during the opening exchanges at Bramall Lane.
An improved second-half showing from United saw them eventually run out 2-0 winners, and move back into the play-off places.
Gibbs-White scored United’s second, rounding goalkeeper Brad Collins to finish in front of the Kop after Sander Berge had put the Blades ahead.
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Victory ended a remarkable run of 16 games in 63 days for Heckingbottom’s men, who were left playing catch-up through no fault of their own when a number of games over the Christmas period were postponed.
And the Wolves loanee admitted: “It was really tough.
“We were miles off it in the first half; I think that's due to all the games we've played and the injuries we've had. Just constant games.
“We looked leggy and tired. The gaffer gave us a good telling off in the changing room and we came out fighting and got the win.
“He just wanted us to pull our finger out. We weren’t running, we weren’t tight to people, we were getting played around too easy; he just wanted us to liven up and waken up, and he got us to do that.
“He didn't put it like that but we needed it and it showed in the second half. We came out fighting, we won most second balls and were on the front foot.”
Gibbs-White combined with substitute striker Oli McBurnie for his goal, the striker scooping a brilliant pass over the Reds defence for Gibbs-White to run on to and score.
“It was quite a dry pitch second half,” Gibbs-White added, speaking to SUTV.
“I played it to Oli and saw the space so ran into it. I was screaming for the ball and I wasn't sure I'd get it in time before being offside.
“But it's a great ball in. I just saw the space, took it around the 'keeper and slotted it in.”