This was a rare case of Tottenham turning an injury into a positive. The loss of Radu Dragusin was Dane Scarlett’s cue. Recalled from a disappointing loan spell at Oxford United earlier this month, the 20-year-old striker came on for Dragusin and set Spurs on course to victory over Elfsborg when he headed in his first goal for his boyhood club. It has been almost five years since Scarlett made his debut. He was an unlikely saviour but Ange Postecoglou was not complaining. There was more joy when another substitute, the 19-year-old winger, Oyindamola Ajayi, came on to score on his debut, then when Mikey Moore made it 3-0 with his first professional goal. Spurs had secured their place in the knockout phase. There was relief at avoiding two extra playoff games.

This was only Elfsborg’s fourth competitive fixture since the end of the Swedish season on 10 November. Spurs can dream of the luxury of such a long break. There has been no let-up. The only option has been to play through the pain barrier and although they were boosted by being able to start Micky van de Ven, who came back into central defence after sitting out for over a month, there was a danger that confidence would be on the floor after the shambolic 2-1 defeat by Leicester last Sunday.

The mood felt liable to turn at a moment’s notice. There was backing for the team and the defender was greeted as a returning hero, but the first chants of “Levy Out” were heard as early as the second minute. Postecoglou, meanwhile, looked on edge. It was unusual to see him lose his temper on the touchline and rage at Lucas Bergvall’s positioning in midfield during the early stages. The sense was of a side desperate to release all the negative energy. Spurs made a fast start and looked robust. Van de Ven was there to step in when Elfsborg tried to counterattack. It meant Spurs were more comfortable pushing up, allowing them to exert a smothering high press, and there was no faulting the level of intent in the final third.

The only problem was converting pressure into chances, especially with Elsfborg happy to sit deep and put numbers behind the ball. Space was limited and set-pieces seemed Spurs’ best bet at first. Elfsborg, who began the night just above the bottom 12, were disciplined, physical and happy to deploy their spoiling tactics. There were glimmers for Spurs. Son Heung-min provided spurts of inspiration on the left, dribbling into the area to forge openings. Pape Matar Sarr and Moore both should have profited from the captain’s invention, only for Isak Pettersson to thwart them with superb saves.

Spurs, who are trying to sign the Bayern Munich forward Mathys Tel, could not crack the code before half-time. Richarlison was marked tightly. Pedro Porro surged forward from right-back but his final ball was lacking. Moore was up and down on the right. The ball would not quite fall for Bergvall. It felt tense. There was a rare break from Elfsborg just before the break, but Archie Gray stayed calm and blocked Gottfrid Rapp’s shot.

The intensity had dipped enough for Postecoglou to make a triple change during the interval. Van de Ven was replaced by Dragusin after easing himself back into action, Rodrigo Bentancur came off for Yves Bissouma in midfield and Son made way for Dejan Kulusevski. Spurs were flat at the start of the second half. Elfsborg grew in belief and almost led after 52 minutes. Rapp crossed from the left, Besfort Zeneli’s shot looped off Dragusin and Jalal Abdullai volleyed over from six yards out.

Manchester United and Tottenham cannot meet until the Europa League final after finishing third and fourth in the league phase table. The two Premier League clubs will be placed on different sides of the bracket in Friday's draw, and will both play winners of the playoffs between AZ or Midtjylland and Real Sociedad or Galatasaray. Rangers' final-day climb into the top eight means they skip the playoffs, but they could face the teams they pipped to eighth place – Bodø/Glimt or Anderlecht – while their potential playoff opponents, Twente and Fenerbahce, also look dangerous after just avoiding elimination.

If Rangers advance to the quarter-finals, they are likely to face either Lazio or Athletic Bilbao, although the group-topping Serie A side could play arch-rivals Roma in the last 16. Manchester United and Tottenham will be in a quarter with Eintracht Frankfurt or Lyon, depending on the draw's outcome. The game was drifting. Porro drove in a cross for Bergvall to head at Pettersson. Then came a familiar sight: the physio running on to tend to a Spurs player, Dragusin calling for treatment after appearing to jar a knee while carrying out a routine clearance.