The Blades had been bottom of the pile since September 23 but four points in the last two games before November's international break have lifted them above Burnley and to within four pioints of their next opponents, Bournemouth.
Brighton totally dominated the first half but only had Simon Adingra's goal to show for it. And when Mahmoud Dahoud was sent off after 69 minutes, the visitors pounced, forcing Adam Webster's own goal when he put Jayden Bogle’s cross through his net just five minutes later.
Whilst their was much talk afterwards about the league position and the first away win of a difficult Premier League campaign, Heckingbottom insisted it was window dressing.
"It's sort of irrelevant," he said. "What is pleasing is how we've played against a good team. I felt they were very good how they started the game, caused us problems.
"We showed a lot of character to stay in the game but it was more the composure even in the first half when they had so much of the ball, we started to control where we had it, just over the centre circle and I think that realisation allowed us to change a couple of things and affect their first pass.
"So the important thing was staying in the game."
He was pleased with the way his side kept their composure during a first half where Brighton had 72 per cent of possession.
"I thought Brighton started the game really well," he said. "We're disappointed with the goal but I have to look past that and the first 25 minutes in particular they moved us about and exploited the spaces.
"We tried to be aggressive with it but you can sort of pre-empt what they're going to do but the players on the pitch for them solved the problems as well. They kept moving us about too much, too often and exploiting the space.
"The good thing was I thought we showed a lot more calmness as the game went on which meant we were more comfortable with them having the ball but having the ball in front of us. It was really important we stayed in the game and we got to half-time and could make two real simple changes without the ball, which helped us.
"We certainly needed a better first pass when we won the ball back and in possession in the first half even when we were composed and got on the ball, nine times out of 10 we'd end up back at Wes (Foderingham, their goalkeeper), he'd have to go long and we'd give them the ball back.
"Second half we needed the same composure on the ball bit more bravery to be the one playing the pass to the front three or the wing-back. That then allows us to play the game in their half a lot more.
"Second half I was pleased with all of it. We're going to make mistakes but my expectation was we were brave when we get on the ball, we try and get forward and commit bodies. I can't be criticising them when we're sloppy trying to do that."
The Blades had also sat in before coming into their own when they beat Wolves at Bramall Lane for their victory of the campaign eight days later.
"The pleasing thing for me is certainly in the last two games it's been us the stronger team finishing the game,” said Heckingbottom, whose team beat Wolves with a stoppage-time penalty.
"You're not getting in front and clinging on – although I want us to do that as well.”