It was left to the kids to soothe the angst in N17. After the introspection brought on by a dismal run of form, it was at least heartwarming for Tottenham to seal their place in the last 16 of the Europa League thanks to three academy products puncturing the tension during a blistering end to an otherwise forgettable game.

This was not a night to rage at Daniel Levy, the beleaguered Spurs chairman. This was a night that belonged to Dane Scarlett, who did not look like a saviour when he came on with the score locked at 0-0 on 66 minutes. Inspiration was running low at that stage. Radu Dragusin had just added to the injury problems after jarring his knee and the underdogs of Elfsborg were beginning to think that there might be a goal in it for them.

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But Scarlett wanted it when he replaced Dragusin. Recalled this month from a disappointing loan spell at Oxford United, the 20-year-old striker immediately threw himself into the thick of the action. This was Scarlett’s chance. It has been almost five years since he made his debut for Spurs and he was desperate to impress. The desire was clear when Dejan Kulusevski crossed in the 70th minute and Scarlett, who cannot go back out on loan now that he has played for two clubs in one season, held off a challenge before making it 1-0 with a fine header.

Ange Postecoglou’s faith in youth had been rewarded, and there was more to come. There was more joy when the 19-year-old winger Oyindamola Ajayi came on to score on his debut. Then came added time and a big moment for the gifted 17-year-old winger Mikey Moore, whose first goal for the club broke Jimmy Greaves’s 67-year-old record as the youngest English scorer in a major European competition.

“Made in Tottenham,” Postecoglou said. “They’ll go to sleep pretty excited. I keep saying that it’s been a pretty tough period in terms of our league form but there has still been real growth. It will all come to fruition. I’m so certain and bullish about that.”

Spurs are 15th in the Premier League but victory here was enough to earn them fourth spot in the Europa League group phase. Postecoglou, who was tightlipped on Spurs’ pursuit of the Bayern Munich forward Mathys Tel, has some respite. He needed his weary team to avoid the drain of falling into the playoff round. He hopes that more players will return from injury in time for the knockout phase, where Tottenham will face one of AZ Alkmaar, Midtjylland, Real Sociedad or Galatasaray. “It’s been a pretty good European campaign,” Postecoglou said. “We’ve had to deal with some adversity.”

Will it be the making of Spurs? There has been no let-up in recent months. They must have marvelled at this being Elfsborg’s fourth competitive fixture since the end of the Swedish season on 10 November. Imagine the luxury of such a long break. Spurs have had to play through the pain barrier and while they were boosted by the return of Micky van de Ven, who came straight back into central defence after more than a month out, there was a danger that confidence would be on the floor after Sunday’s defeat by Leicester.

Lazio finished top of the Europa League's opening league phase despite a 1-0 defeat at Braga. The hosts got the only goal in the sixth minute as Ricardo Horta fired home from Victor Gómez's cross – but it was not enough to send them through as they missed a playoff place on goal difference.

Athletic Bilbao finished second after a 3-1 home win over Viktoria Plzen, with Nico Williams [pictured] opening the scoring after 25 minutes. Roma's 2-0 home win over Eintracht Frankfurt earned the Italians a seeded playoff spot, Angeliño and Eldur Shomurodov goals forcing Frankfurt down to fifth.

Lyon, who were held to a 1-1 draw by Ludogorets, and Olympiakos, who saw off bottom side Qarabag 3-0 with Ayoub El Kaabi striking twice, complete the top eight with Manchester United, Tottenham and Rangers. Bodø/Glimt let a last-16 place slip as they conceded an equaliser away to eliminated Nice.

Hoffenheim earned a dramatic 4-3 win at Anderlecht, but it was not enough to keep the visitors' European bid alive. Tom Bischof and Adam Hlozek helped Hoffenheim take a 4-1 lead, but Anderlecht fought back and missed a late chance to level from a corner and take the final last-16 place from Rangers.

Twente advanced at the expense of Besiktas, Daan Rots' 76th-minute winner earning a home win in a game where both teams needed three points to advance. José Mourinho's Fenerbahce clung on to the very last unseeded playoff spot after letting a two-goal lead slip to draw 2-2 at Midtjylland.

Ajax climbed above Galatasaray among the seeded playoff teams with a 2-1 home win, Kian Fitz-Jim finishing a quick break for what proved to be the decisive goal. Real Sociedad finished in 13th, between those two sides, as Orri Óskarsson's double defeated PAOK Salonika.

Porto edged into the playoffs with a 1-0 win at Maccabi Tel Aviv, ending the hosts' faint chances of progress. Ferencvaros secured their playoff place with a 4-3 win over AZ Alkmaar, Mohamed Ben Romdhane's double giving the hosts a 4-1 lead before two consolation goals in stoppage time. Guardian sport

The mood felt liable to turn at a moment’s notice. There was backing for the team and Van de Ven was greeted as a returning hero, but the first chants of “Levy Out” soon echoed around the ground. The first half was tough. Elfsborg sat back and stifled Spurs. The only rays of hope came from Son, who created chances for Pape Matar Sarr and Moore. Isak Pettersson denied them with superb saves.

The intensity dipped and Postecoglou made 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 Kulusevski, but Spurs were flat. Elfsborg should have led on 52 minutes, only for Jalal Abdullai to volley over from close range.

The game drifted until the familiar sight of a physio running on to treat a Spurs player. Dragusin eventually went off and Postecoglou made the adjustment that turned the game.

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.

With no senior defenders left on the bench, Spurs threw caution to the wind. Scarlett joined Richarlison in attack, Sarr went to left-back, Ben Davies moved next to Archie Gray in central defence and the mood changed. Elfsborg were forced back and they were slow to react when Kulusevski cut in from the right. The Swede’s deep, inswinging cross was a beauty and Scarlett stooped to head in from close range.

Scarlett looked sharp. He was involved again after 84 minutes, finding Ajayi, who dribbled inside and fired in from 18 yards. Nobody was thinking about Levy now. There were more celebrations when Moore ran through to score with another clinical shot.