As much as Ange Postecoglou vehemently insists that Champions League qualification is neither imperative nor the limit of his ambition, he will be hard pressed to find a Tottenham supporter not significantly heartened by their elevated league position after this victory over Nottingham Forest.

With a game in hand over Aston Villa, Postecoglou’s side are now back into fourth – a place they have not occupied since mid-February – and in pole position to feature in Europe’s premier competition next season, notwithstanding some tricky upcoming fixtures. Just do not expect the manager to show any excitement about that fact: “I couldn’t care less about the race for fourth, mate.”

It was not perfect; it rarely is where Spurs are concerned. But unlike in the frustrating draw at West Ham in midweek, they found a way to register what was, in the end, a fairly comprehensive scoreline.

It might have been entirely different had Forest benefitted from a couple of major first-half incidents. With the scoreline level after Chris Wood had cancelled out an early Murillo own goal, the New Zealander spurned a glorious chance for his second when crashing the Spurs post with a sledgehammer two yards from goal when a gentle stroke of the paint brush would have sufficed.

Ten minutes later, Forest captain Ryan Yates went down holding his stomach after an off-the-ball incident with James Maddison. Replays showed a rather suspicious-looking fist connecting with Yates’s midriff, but the Spurs midfielder escaped punishment.

“He punched him,” said Nuno Espírito Santo. “I was surprised that VAR didn’t tell Simon [Hooper, the referee] to review it better because, honestly, with all respect, Maddison loses his composure and it’s a punch in the stomach to Yates. It should have been reviewed and a different decision. It’s clear from me. It is a red card.”

At that stage, Spurs were floundering after their bright start. But a change to both central midfielders at half-time sparked a wholesale improvement from Postecoglou’s side in a second period in which the hosts were rarely tested. Tottenham settled matters soon after the break through a couple of thunderbolts from the unlikely figures of Micky van de Ven and Pedro Porro.

“Today had a little bit of everything for us,” said Postecoglou. “We started the game well, not just the goal, and controlled it well. We lost our way a little bit towards the end of the first half, but it was a super reaction and the whole second half we were really dominant. We played some good football, scored a couple of goals and created a couple more against a team that is desperate for points and fighting for everything. I thought we handled it really well.”

Based on the opening 45 minutes alone, there was every chance that Nuno’s first return to the Tottenham Hotspur Stadium since setting an unwanted record as the club’s shortest permanent manager might prove fruitful.

Having registered only a second league win this calendar year earlier in the week against Fulham – a continuation of a mini resurgence since Forest were deducted four points for breaching Premier League finance regulations – the visitors almost went ahead in spectacular fashion through Murillo. The Brazilian lobbed Guglielmo Vicario with his audacious effort from somewhere approaching 70 yards, but the ball bounced wide.

He did find the net four minutes later, only at the wrong end. Continuing his fine run of form, Timo Werner fizzed a tricky low cross across the six-yard box, which was turned in by the Brazilian’s outstretched boot.

Matz Sels did brilliantly to deny Brennan Johnson from point-blank range 10 minutes later and Forest soon found an equaliser. A lovely one-two between Anthony Elanga and Neco Williams culminated in the Swede squaring across goal where Wood turned it into the far corner.

It was the Kiwi’s fourth goal in as many games since returning from a hamstring injury, but how he did not add to that tally when blasting against a post minutes later flummoxed all inside the stadium after Vicario had saved superbly from Yates’s shot.

If the home fans went into half-time concerned that their team might be about to drop more points in the Champions League race that Postecoglou refuses to acknowledge, their fears were swiftly assuaged.

First, Van de Ven thumped in from the edge of the penalty area after some patient buildup from a Spurs corner. Then, Maddison’s cross was flicked on by substitute Rodrigo Bentancur for Porro to drill home. The victory margin would have been even greater had Sels not pulled off a great save to turn Son Heung-min’s late shot on to a post.

“The first half was very good,” said Nuno, whose Forest side are teetering above the relegation zone on goal difference alone. “We controlled Tottenham, we had good spells, we scored, we had chances. Our major challenge is to reproduce this 45 minutes for the whole game.”