Swansea may sense that wizardry is not confined to a solitary Potter. Relegated and eviscerated by an exodus, trailing to a more experienced Sheffield United side, seemingly set for an unpleasant time in the Championship, their callow team instead invoked a victory that owed much to their new manager.

Graham Potter marked his bow with the most decisive of substitutions, though he had to share the limelight with another newcomer. Yan Dhanda’s first-team career was 29 seconds old when, with his first touch of the ball in professional football, he steered in the winner.

If the focus has been on Swansea’s summer sales – a contingent who may be swelled to include Sam Clucas and Federico Fernández – the arrivals have been obscured. Sheffield United were not alone in not noticing Dhanda, a 19-year-old lured south from Liverpool.

Potter modestly attributed his introduction to the fact Jay Fulton was struggling but noted: “He is an attacking sub at 1-1. He is not going to help much if the ball comes into your box, bless him. It was a bit of a gamble.”

It paid off. The finish came from Dhanda’s right boot, but it nonetheless had Potter’s fingerprints all over it. “You can’t do anything with 11 players,” the manager added. “You need your substitutes to have an impact.” They did. The initial incursion was made by Jefferson Montero, another influential introduction. His cross was met by Barrie McKay, switched to the right flank by Potter in a reshuffle. While he was fouled by Jack O’Connell, Dhanda spared the referee, Jeremy Simpson, a decision by sweeping in the loose ball.

If his input was improbable, so was the result. Swansea’s only victories in a difficult pre-season came against Yeovil and, in a behind-closed-doors friendly, Newport County. Summer sales meant that only three players – Martin Olsson, Tom Carroll and the new captain Mike van der Hoorn – started their final Premier League game against Stoke and Saturday’s match at Bramall Lane.

At just 23, McKay found himself the senior member of a front four featuring three debutants. The Scot proved ubiquitous in the second half. He had been pencilled in to play 70 minutes but Potter was rewarded for his flexible thinking. The inventive, elusive McKay helped supply Oli McBurnie’s 71st-minute leveller, exchanging passes with the striker and mustering a shot that the borrowed Manchester United goalkeeper Dean Henderson did well to save. McBurnie nevertheless converted the rebound for his first Swansea goal. He is charged with leading the line, the role Tammy Abraham and Jordan Ayew took last season. Both managers applied the same adjective to his display. “Outstanding,” Potter said.

McBurnie almost added another goal, a deft header just missing the far post, while McKay rattled the bar, 12 minutes after his scheduled departure, before Dhanda got United’s danders up. “Two poor goals,” said Chris Wilder, their manager. “I don’t think we should be expecting just to steamroller a side that has just come out of the Premier League. They have got World Cup players.” He was citing Olsson, though a World Cup semi-finalist – the former United defender Harry Maguire – was among the watching Blades left disappointed by the scoreline.

The subtext to Wilder’s comments was that, 15 months ago, United were a League One side, two divisions below Swansea. He also lamented the chances squandered by David McGoldrick and a wasteful John Lundstram before George Baldock gave his side the lead, the right wing-back meeting a cross from his left-sided counterpart, Enda Stevens, to illustrate the threat of Wilder’s defenders.

“The goal knocked us,” Potter said. “You have got a choice whether you cave in or respond. The character of our players was amazing.” They still relied on goalkeeper Kristoffer Nordfeldt to spare Connor Roberts an own goal and deny United an equaliser.

So Swansea could savour what ranked as an improbable sequel. They came full circle, seven years after their previous Championship game brought victory over United, leading to 2011’s successful play-off campaign. Potter’s last game in England had produced a win away at Arsenal for the unfancied Swedish side Östersund. His next produced a different kind of magic, even if one man was not cast under the new Swansea manager’s spell. A blunt Wilder said: “I’m not really bothered talking about Graham Potter.”