Behold the steelier, sturdier, more structured version of Angeball. From opting for the power of Pape Matar Sarr over the silkiness of James Maddison in midfield, to finding the right motivational words when all looked lost at half-time, this was a good day for Tottenham’s romanticist of a manager.

Ange Postecoglou’s substitutions were spot-on, his tactics proved far more effective than Unai Emery’s anti-football approach, and Aston Villa, their legs heavy after being given the runaround by Sarr, simply had no response to a stirring comeback from Spurs in the second half.

Related: Tottenham 4-1 Aston Villa: Premier League – live reaction

In the end it felt like a victory for earning the right to play. While Villa set out to spoil, carving out a lead when a set-piece routine led to Morgan Rogers scoring just after the half hour, Spurs married their creativity with a physical edge. Their second goal, claimed by Dominic Solanke with a delightful dink over Emiliano Martínez, was a case in point: Dejan Kulusevski’s glorious through‑ball had created the opening but it was significant that the move began with Ben Davies forcefully dispossessing Ollie Watkins and Sarr overwhelming Villa with one of many bursts through the middle.

“We accept the result,” Emery said, making no excuses after seeing his side miss the chance to go third. There were too many mistakes from Villa, who looked jaded despite resting players during their midweek defeat against Crystal Palace in the Carabao Cup, and Spurs pounced.

Brennan Johnson equalised early in the second half, Solanke added a quickfire double after fine work from Sarr, and there was even time for Maddison, who remained on the bench until the 82nd minute, to round off the scoring with a gorgeous free-kick deep into added time.

Not that Postecoglou, whose team rose to seventh, was getting carried away. He was criticised after the insipid 1-0 defeat at Palace last week, since when Spurs have knocked Manchester City out of the Carabao Cup and made a mockery of Villa’s top-four aspirations. “You don’t fall off cliffs and you don’t fall off mountains within a week,” Postecoglou said. “It’s all part of the same process.”

Progress here was measured by whether Spurs could grind with Emery’s streetwise team. Postecoglou had adjusted his tactics accordingly, Maddison sacrificed for the double bolt of Sarr and Rodrigo Bentancur in midfield, but it was attritional at first.

Spurs were restricted to hopeful efforts from distance and the crowd’s anxiety was palpable. Everyone could see what Villa wanted to do. They were happy to disrupt play with a series of niggly fouls and there was no sign of their signature high line. Emery had no desire to give Son Heung-min and Johnson space to run behind on the flanks.

The half played out in predictable fashion, Villa biding their time before winning a corner in the 30th minute. Cue panic. Cue Austin MacPhee, Villa’s set-piece coach taking centre stage. The first ball was cleared but it came back to Lucas Digne. He lifted in a high cross, Amadou Onana headed against the woodwork and Spurs scrambled the ball behind.

The pressure grew, Villa pressing at an obvious weakness, Rogers pinning Guglielmo Vicario to his line. The goalkeeper was blocked off and Spurs cracked when Digne delivered an inswinging cross to the near post. Vicario stopped Bentancur from scoring an own goal but Rogers smashed the rebound into the net.

There was not much conviction to Spurs’ appeals for a foul on Vicario. The concession unnerved them and they could have fallen further behind, only for Watkins to scuff wide from an inviting position.

It was a pivotal miss. Spurs raised the pace after the break and they levelled in the 49th minute. Son’s cross from the left was a beauty, Pau Torres and Ezri Konsa taken out of the game as Johnson arrived at the far post to convert.

Emery urged calm. The action was frenetic, though, and Martínez had to save well from Solanke. Cristian Romero injured himself in the process of cleaning out Rogers.

With Radu Dragusin deputising for the injured Micky van de Ven, Spurs played with their second-choice centre-back pairing after Ben Davies came on for Romero. Emery introduced Jhon Durán on for Rogers. Postecoglou had brought on Richarlison for Son, who looked unimpressed with the idea that he was being protected after his recent injury problems.

But while Son muttered to himself on the bench Spurs found a second wind. As the minutes ticked away, Davies stepped out to challenge Watkins. Sarr drove forward, linking with Johnson before Kulusevski flummoxed Villa with a reverse pass to Solanke, who beat Martínez with a cool finish.

Spurs had the clarity and belief. They went for Villa again, Sarr intercepting a loose pass from Torres and finding Richarlison, who crossed for Solanke to score again.

Emery was slumped in the dugout by the time Maddison bent in the fourth. Spurs were rampant, Villa overrun.