Tottenham were heading for their first Premier League defeat under Ange Postecoglou as they trailed to Gustavo Hamer‘s goal against the run of play in the 75th minute.
But second-half substitute Richarlison ended his goal drought with the equaliser in the eighth of 12 minutes added on.
He then set up Dejan Kulusevski for the winner two minutes later as Tottenham made it four wins in a row and 13 points from 15 — their best start to a top-flight season since 1965-66.
Tottenham are second in the table, two points behind champions Manchester City.
“All the subs that came on made an impact. For Richy, it was the point I was trying to make. You try to have the balance in life,” Postecoglou told reporters.
“His football hasn’t been that bad and while things can happen in life, the football is what he can control.”
Sheffield United, still without a league win this season, had Ollie McBurnie sent off for a second yellow card for arguing with the referee as their frustration boiled over.
Brazil forward Richarlison had endured a testing time of late, unable to nail down a starting place at Tottenham and in midweek saying he would seek psychological help after looking tearful when substituted in Brazil’s game against Bolívia.
He was one of three Postecoglou substitutions in the 80th minute as Tottenham threw everything at the Sheffield defence.
And he delivered his first Premier League goal since April as he found space in the area to head in a corner swung across by fellow substitute Ivan Perisic.
Tottenham sensed their chance to snatch all three points and it was Richarlison whose pass enabled Kulusevski to hammer a shot into the corner and send the home fans wild.
“Great ending. In terms of what we’re trying to build, there’s the football side but also it’s about building the spirit and togetherness at the club,” Postecoglou said.
It had looked as though Sheffield United would return with the points having pulled off the ultimate smash and grab raid.
Tottenham had 28 goal attempts, 16 of which were in the second half, and 70% of the possession but were stunned when Hamer gave the stubborn visitors the lead with a shot that crept in off the post.
Visiting keeper Wes Foderingham made some fine saves and United rode their luck at times with Richarlison also heading a chance over the crossbar but the Spurs fans were singing the Brazilian’s name at the end.
It was despair for the visitors who have one point from five games. “We had to concentrate all game, it was a fatigue thing, the pressure they put on us,” manager Paul Heckingbottom said.
“Two lapses and we’ve been beaten 2-1. To lose a game in that way is really cruel. But it doesn’t change our performance.”