Tyler Adams struck two minutes from time to send Leipzig through to the semi-finals for the first time.
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Leipzig will face Paris in the last four of the UEFA Champions League after sealing a late 2-1 victory against Atlético.
Match in brief
Marcel Halstenberg served early warning of Leipzig’s intent when he volleyed over in the fourth minute, though it was Yannick Carrasco’s powerful first-time shot which required the smartest stop of the first half; Péter Gulácsi was up to the job.
Julian Nagelsmann’s side did take the lead soon after the break, though, Marcel Sabitzer fizzing in a cross from the right which Dani Olmo instinctively and expertly headed past Oblak.
João Félix’s introduction from the bench added life to Atleti and it was little surprise when one of his surging runs into the penalty area forced Lukas Klostermann to bring him down. The 20-year-old Portugal forward dusted himself off before firing beyond Gulácsi’s reach from the spot.
Extra time was looming large until Angeliño’s square pass from the left picked out Tyler Adams, who took one touch to set himself and another to strike low into the net via a sizeable ricochet off Stefan Savić. A good time to score his first goal for the club.
Man of the match: Dayot Upamecano (Leipzig)
Roberto Martínez, UEFA technical observer: "An outstanding defensive display, keeping Atlético's attacking threat to a minimum and winning every challenge in one v one situations. Threatening in both boxes, he showed the perfect mixture of defensive aggression and composure on the ball."
James Thorogood, Leipzig reporter
In the biggest game in the club’s history, Leipzig produced a near-flawless performance, but for the blemish of a clumsy challenge from Klostermann. They stuck to their game plan and believed in their abilities despite the setback. Now they’ve knocked out two former finalists to reach the final four of the Champions League just four years after securing Bundesliga promotion for the first time in club history.
View from the stadium: Joe Walker, Atlético reporter
It is not often in recent years that Diego Simeone has been outsmarted by his opposite number at this stage of the competition, but you have to doff your cap to Nagelsmann and his young, exciting Leipzig side. They hounded Atleti and did not give them any time or space to breathe, penning their more experienced opponents back and dominating them for long periods.
Julian Nagelsmann, Leipzig coach: "We didn't create many chances in the first half but we defended very well. You don't get many opportunities in the final third against Atlético. Our offensive game was the difference today; Atlético didn't have many chances and we created more."
Tyler Adams, Leipzig midfielder: "We're really, really excited. We know Paris are a great team, we saw what they did against Atalanta yesterday and they've got really good players."
Diego Simeone, Atlético coach: "We gave it everything we had. There are no excuses. We gave our best and made it to the quarter-finals. We are going out fairly and we have to congratulate our opponents."
- Leipzig are the 32nd team to reach the Champions League semi-finals.
- Leipzig are the 75th team to reach a European Cup semi-final, and the first newcomers since Manchester City in 2016.
- As well as being his first for Leipzig, Adams' goal was also his first in the competition.
- Dani Olmo's goal was his first in the Champions League for Leipzig and came on his European debut for the club.
- Captain Koke made his 457th Atleti appearance, putting him in outright fourth position in the club’s all-time appearance rankings.
- João Félix has scored four goals in his three European quarter-final appearances, having hit a hat-trick for Benfica against Eintracht Frankfurt in last season's UEFA Europa League first leg.
Leipzig: Gulácsi; Klostermann, Upamecano, Halstenberg; Laimer (Adams 72), Sabitzer (Mukiele 90+2), Kampl, Angeliño; Olmo (Schick 83), Y Poulsen, Nkunku (Haidara 83)
Atlético: Oblak; Trippier, Giménez, Savić, Lodi; Carrasco, Saúl, Herrera (João Félix 58), Koke (Felipe 90+2); Costa (Morata 72), Llorente
Leipzig will take on Paris in the semi-finals. Their single-leg tie will kick off at 21:00 CET on Tuesday 18 August and be held at the Estádio do Sport Lisboa e Benfica in Lisbon. The teams have never met before.