Chants of “Daniel Farke, Daniel Farke” rang out from the travelling faithful after this seismic Leeds win lifted them six points clear of Tottenham, whose plight darkens further after the visitors pulled off a first league win at Old Trafford since February 1981.

It means Michael Carrick has lost a home game for the first time as Manchester United’s interim manager. His team lacked control throughout, a state not aided by Lisandro Martínez’s silly 56th-minute red card for yanking Dominic Calvert-Lewin’s ponytail, and he is now suspended for three matches, though the club may appeal.

By the time of the defender’s marching orders two Noah Okafor strikes had Leeds cruising and while the hosts rallied, Casemiro’s header proved a consolation only.

Yet if Carrick’s men remain likely to seal Champions League qualification, Leeds motored home cock-a-hoop and if they beat Wolves on Saturday before Spurs play Brighton then they may feel out of the relegation dogfight.

Karl Darlow (centre) and Ethan Ampadu (left) revel in a long-awaited Leeds win at Old Trafford. Photograph: Phil Noble/Reuters

At kick-off and three points above 18th-placed Spurs, Leeds surely contemplated the draw they achieved in January’s reverse fixture acceptable. Leeds’ previous league win was on 6 February and as they had drawn seven of their last eight away games (losing the other) three points appeared unlikely.

The first half suggested the opposite. After Manuel Ugarte, who struggled throughout, lost the ball Leeds pinged it about, eventually raiding along the left through Gabriel Gudmundsson. The wing-back crossed and Calvert-Lewin’s point-blank stab was repelled by Senne Lammens.

Better followed inside five minutes, this time from the right. Jayden Bogle skipped beyond Luke Shaw and, as Ugarte tracked him, he hit an inviting ball: Leny Yoro – inadvertently – flicked it on to Okafor and he steered home. Afterwards, Carrick pointed to a “forearm smash” to Yoro’s head by Calvert-Lewin but there was no review.

The strike had the Swiss offering a nonchalant hands-folded celebration, and was regaled with “marching on together” and “Yorkshire, Yorkshire” by the delighted fans. The hosts were stung and stunned. A Noussair Mazraoui-Amad Diallo-Bruno Fernandes break took them into Leeds territory. Then, Diallo’s pirouette-and-shot forced Karl Darlow to dive right to save. The hosts had found some tempo, their crowd, on this temperate spring evening, upping noise in response.

Carrick plumped for Benjamin Sesko as his No 9, dropping Bryan Mbeumo. He raced through the middle for Diallo’s threaded ball. But he hesitated and on unloading, the ball dribbled into Darlow’s gloves.

Bruno Fernandes assisted yet another goal, but even his efforts were not enough to prevent the loss. Photograph: Adam Vaughan/EPA

This was a contest of transitions that Carrick did not enjoy as he craves control. The 41-year-old drafted Ugarte in for a first league start since January, owing to the “small issue” that ruled Kobbie Mainoo out, and the Englishman’s calm head was missed.

Leeds dominated, carrying a serial threat to their hosts, as their second proved. Here, a flurry of activity in the area featured Calvert-Lewin losing Jayden Bogle’s cross, the ball pinging about, and Brenden Aaronson’s effort being blocked.

Eventually, from range, Okafor netted a second: his long-range shot skimmed off Yoro and to the goalkeeper’s left. Carrick hung his head, Farke was happy, and the jubilant visiting support repeated: “We are Leeds, we are Leeds”, as they stared at a memorable – and vital – win.

United, momentarily, sparked when, at a corner, Matheus Cunha blazed from distance, but there was zero pattern to their play. Instead a near-franticness played into Leeds’ muscular and feisty mode.

Martínez, in for the suspended Harry Maguire, made a goalline stop to keep Ao Tanaka from making it 3-0, and so Leeds wandered off at the break rampant, with their hosts in the mire.

Carrick may have dished out the rollicking he says he can when needed as Sesko thundered in on goal soon after the restart. Shaw’s curving ball down the left took the centre-forward in but the onrushing Darlow thwarted a clean connection and Leeds escaped.

Now, disaster for Manchester – plus a touch of farce – as Martínez was sent off by Paul Tierney, the referee reviewing the pitchside monitor and deeming the defender’s grip of Calvert-Lewin’s hair worthy of marching orders.

Lisandro Martínez employs unconventional defensive measures to try to stop Dominic Calvert-Lewin in the second half. Photograph: Phil Noble/Reuters

The mild-mannered Carrick was angered – “a shocking decision” his verdict – Martínez seriously unhappy, and those in red were down to 10 men for the 34 minutes left of regulation play. Casemiro moved back to partner Yoro in central defence yet neither of them nor the rest of the rearguard could prevent Gudmundsson waltzing through and shooting.

While Lammens’ goal was not in peril, Leeds’ net was when Cunha controlled Shaw’s chip and took aim, Darlow flying right to save, in what was still a quasi-basketball affair.

Next, a lifeline: Fernandes floated in a cross and Casemiro’s header rippled the net. On came Mbeumo and he and Cunha spurned openings, before Darlow beat away a Sesko header and Casemiro’s effort was cleared off the line, in a breathless finish.

At the final whistle Farke sank to his knees and roared – he and his players know how precious these three points are.