Roberto De Zerbi had said he wanted no crying in his camp after Brighton scored their late equaliser last week, and it was just as the Wolves fans had started chanting “You’re going to cry in a minute” that the substitute João Palhinha struck the goal that briefly helped Tottenham climb out of the relegation zone and avoid a club record of 16 consecutive league games without a win.

The Spurs manager ran on to the pitch, pumping his fists, after the Portugal midfielder, played onside by the former Spurs defender Matt Doherty, slid in to score after Richarlison had scuffed a shot goalwards when Pedro Porro’s corner fell his way in the 82nd minute.

When news of Everton’s equaliser at West Ham then broke, the Spurs fans were celebrating as if final-day salvation was secured. Their joy was short-lived as West Ham then went back in front to move two points ahead in this two-way tussle to avoid the final relegation berth, but at least the Spurs manager has the first of the five wins he is targeting to keep his team in the Premier League.

Even losing Dominic Solanke and Xavi Simons to injury, taking the absences to 11, could not prevent De Zerbi celebrating his first win as Spurs manager, and the club’s first in the Premier League since 28 December.

Perhaps the Spurs players were mentally boosted by seeing an advert for a performance psychologist appear on their LinkedIn feeds a month from the end of the season. Certainly, buoyed by their performance if not the result against Brighton, they were the better side in the opening stages against a Wolves side whose relegation was confirmed earlier in the week.

De Zerbi only had to make the one enforced changed – Djed Spence replacing the injured Destiny Udogie at left-back – as he built on the positivity he is intent on instilling. Even James Maddison, on the bench again for his charisma if not his fitness, remained in the squad. Never let the small matter of recuperating fully from a ruptured ACL get in the way of good vibes.

Wolves have looked like a decent mid-table team for much of this second half of the season, but their disastrous start has left relegation a formality for some while. After resounding home results against Arsenal, Aston Villa and Liverpool, the long break from mid-March seemed to suck the life out of them with so little in the table to play for. Having overcome Derby’s record low Premier League tally of 11 points, pipping Burnley to 19th place only holds so much glamour. They have lost three successive games to bottom-six sides since, West Ham, Leeds and now Spurs playing with the edge of teams with much more to play for.

Wolves belatedly realised they had to produce some fighting spirit in this game, with João Gomes showing the class on the ball in tight spaces that has led to strong interest from Atletico Madrid. The South Bank relished the prospect of playing “[West Bromwich] Albion away, ole ole”. They later edited this to “Tottenham away” as Spurs slipped back into the bottom three with West Ham winning.

Either side of half-time, Solanke had to go off, possibly with a hamstring injury, while Randal Kolo Muani was replaced by choice, before Simons went down, as Hugo Bueno saw the ball out for a goal-kick, and even the Wolves players were calling for medical help.

Good luck to Sebastian Kehl, the former Borussia Dortmund sporting director, or whoever comes in as Spurs’ new co-sporting director charged with helping rebuild the playing squad.

Meanwhile, Wolves started to show some goal threat: Mateus Mane headed over; Adam Armstrong almost cashed in as Kevin Danso dithered over a difficult ball back to Antonin Kinsky. Hugo Bueno curled one free-kick just over, while Kinsky saved superbly from João Gomes’ effort in the 98th minute. Even though Wolves were no great shakes, it felt as if Spurs had been getting worse before the late charge.

Rodrigo Bentancur had come as close as anyone to scoring when he produced a powerful header from Porro’s free-kick, José Sá saving superbly, before Doherty flicked the ball away just as Richarlison looked about to head home. Then came Palhinha’s decisive intervention.