Nuno’s side piled on the pressure and were eventually rewarded with a fine goal from a corner, with Saiss glancing home in the 86th minute with the ball nestling into the far corner.
The performance and result, which meant Spurs failed to make up ground at the top of the table, will bring Jose Mourinho’s approach into sharp focus as they threw points away from a winning position for the fourth time this season.
Victory would have taken Spurs third, four points off leaders Liverpool, but they showed no ambition to add to their early goal, which came inside the opening minute.
Wolves might even have snatched the win at the death, only for Fabio Silva fluff a header from close range.
But it was Spurs who got off to the perfect start.
After Son Heung-min broke the offside trap to win a corner the ball fell to Ben Davies at the far post and he teed up Ndombele, whose low 25-yard shot went through a crowd of bodies and into the bottom corner.
The Frenchman was showing just why Spurs paid a club record fee for him 18 months ago as he was running the show, playing a key role in Spurs’ transition from defence to attack.
He manoeuvred through a crowd of bodies to set off an attack, which ended in him crossing for Sergio Reguilon to nod an effort just wide, before carrying the ball 40 yards to create a three-on-two situation, only to choose the wrong option in passing to Reguilon instead of Harry Kane as the Spanish wing-back fired straight at Rui Patricio.
But there was little further attacking intent from Spurs and Wolves began to stir.
They were causing the visitors problems out wide, in particular down the right where they fashioned two chances to equalise.
First Nelson Semedo was allowed space to cross and he found Silva, who rattled a shot just wide of the near post.
Then an even better opportunity came to Daniel Podence five minutes before the break as a weak Davinson Sanchez header fell perfectly to him but he put his shot straight at Hugo Lloris.
Just as they did at Palace earlier this month, Spurs invited Wolves on to them in the second half and the hosts did not need asking twice as they turned up the pressure.
They did not cut their visitors open and came closest with shots outside the area as Ruben Neves and then Pedro Neto had goalbound efforts deflected over.
Neves again had an opportunity from distance as he tested Lloris, but the France goalkeeper was equal to it with a smart save down to his left.
There was an air of inevitability about Wolves’ equaliser which came four minutes from time.
Saiss darted to the near post and sent a glancing header inside the far post as Spurs’ weakness from set-pieces was highlighted again.
The hosts were the ones pushing for the winner and it could have come right at the death, but Silva did not connect properly with a header and Mourinho’s side clung on for a point.
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