Disciplined, unfussy, a little scrappy and garnished with a dollop of luck. Tottenham have rarely known afternoons such as this under Ange ­Postecoglou but they summoned a textbook away performance, rolling up their sleeves and putting a halt to the previous seven weeks’ freefall.

Spurs had not won a league game since 15 December, and that was against the flimsy proposition of ­Russell Martin’s Southampton. This time they dealt with one of the division’s most exacting physical examinations and there was no doubting the importance to their manager, who leapt off his seat and punched the air when Pape Matar Sarr put matters beyond doubt late on.

Related: Brentford 0-2 Tottenham: Premier League – live reaction

It will not remove the unease around Tottenham, which was demonstrated by regular chants from the away ­section demanding that Daniel Levy step down. But they had to start somewhere and, with the Austria defender Kevin Danso arriving from Lens and a move for Axel Disasi in their sights before the transfer deadline on Monday, Postecoglou might feel cautious optimism that the darkest hour has passed.

Brentford might fear theirs is to come after a fourth home defeat in five. They were dominant between the boxes but failed where it counted in both. A flap by their goalkeeper Hákon Valdimarsson, leading to an own goal from Vitaly Janelt, brought Spurs’ opener and Yoane Wissa was far from his clinical best at the other end. Thomas Frank lamented a “missed opportunity” afterwards but their threat faded in the game’s last quarter and by the close they were reduced to wild swipes at goal.

“In the context of where we are, it’s an important one,” Postecoglou said of three points that had hardly been nailed on at the outset. Spurs had started with another makeshift back line, Micky van de Ven not deemed ready to build on his comeback against Elfsborg and Radu ­Dragusin sidelined with what may be a serious knee injury. “It doesn’t look good,” Postecoglou said of the Romanian’s problem, which will be assessed by a specialist on Monday.

It meant another deployment at centre-back for Archie Gray, whose performance was impeccable. Frank said Spurs’ defending of the penalty area was “some of the best I’ve seen all season”, which would ordinarily require a double take. The 18‑year‑old did not put a foot wrong, a first-half block from Kevin Schade’s goalbound shot among numerous interventions that required bravery and immaculate ttiming.

At left-back, the once maligned Djed Spence restricted Bryan Mbeumo to two or three dangerous deliveries. What was, on paper, a mish-mash had earned their fortune. “He’s had to bide his time,” Postecoglou said of Spence. “We needed him to become patient but also to mature a little bit. He’s one of those defenders who loves to take on the elite.”

Perhaps the post-match readings would have been different if Wissa had converted one of those Mbeumo crosses early on, instead heading over. Spurs had barely threatened in the first half-hour, some Dejan Kulusevski flashes aside, but a rare sortie saw Yves Bissouma’s shot deflected for a corner. Son Heung-min’s ball in from the left was devilish but Valdimarsson, playing due to Mark Flekken’s injury, had to be stronger. He was boxed in by Bissouma, who is hardly a colossus, and could not intervene before it cannoned in off the back of an unwitting Janelt.

Give or take a few centimetres, the adage about settling for a ­winner off someone’s posterior seemed to ring true. Postecoglou would ­certainly have taken that and his players set about protecting it, Antonin ­Kinsky proving more resolute than his opposite number when batting away a vicious drive from Christian Nørgaard. A similarly rasping effort from Mbeumo rapped straight into the head of Richarlison, who came off mercifully lightly.

At half-time Postecoglou swapped Mikey Moore, a ­marvellous ­talent unsuited to this particular ­assignment, for the relative veteran Lucas Bergvall. The Swede shot narrowly wide, as did his ­compatriot Kulusevski, but otherwise it was sleeves‑up time.

Wissa surely had to equalise in the 54th minute after Schade had flicked on a ­Mikkel Damsgaard cross but, in front of goal, blasted over via the top of the bar. Set-pieces rained in, most of them repelled ­convincingly, and a Mbeumo attempt that spun out for a throw-in came to epitomise the sapping of Brentford’s belief.

They had one last chance when Spence hacked away Fábio ­Carvalho’s overhead kick from near the line. Almost immediately Spurs sprang forward, slick work from Rodrigo Bentancur and, latterly, Son, feeding Sarr. A nudged finish ensured Postecoglou could celebrate.

“Credit to the boys, they were brilliant,” he said. “The players have been hurting and I’m sure the ­supporters are.” Those fans milked the ­occasion, serenading the victors with ­renditions of “We are staying up”. Baby steps indeed, but this one was exactly that Tottenham needed.