The Nerazzurri won the first leg 1-0 thanks to a late Marko Arnautovic strike, but the Austrian was injured along with Carlos Augusto, Stefano Sensi and Juan Cuadrado. The hosts missed Thomas Lemar and Marcos Paulo, but Antoine Griezmann returned almost a month after an ankle sprain.
Atleti didn’t have a single shot on target in the first leg, but tested Yann Sommer within five minutes here with a Samuel Lino angled drive at the near post.
Denzel Dumfries also forced a double save from Jan Oblak after running onto the Hakan Calhanoglu pass, while Lautaro Martinez’s deflected effort did not surprise the goalkeeper.
Sommer smothered the free header from ex-Juventus striker Alvaro Morata, but Inter took the lead instead with a well-worked move.
Nicolò Barella ran onto a ball down the left and found Dimarco with a slide-rule pass, which the wing-back steered in first-time with the inside of the right boot from 12 yards.
It lasted barely 120 seconds before Atleti responded, as Benjamin Pavard shinned the clearance on a Koke assist, it hit Alessandro Bastoni and landed kindly for Griezmann to fire in from close range.
Pavard made up for it with a crucial block as Griezmann dribbled between defenders and after the restart Sommer was glad Griezmann scuffed the finish from 12 yards.
Morata should’ve left the roll across for Griezmann behind him, but instead shinned it over the bar, while Rodrigo Riquelme’s solo effort was deflected just wide off Pavard.
Inter really should’ve restored their lead on 76 minutes when breaking on the counter from a corner, as Lautaro Martinez’s pass allowed Thuram to spring the offside trap, only to then balloon over the bar.
Matteo Darmian came off the bench and made a decisive block inside the six-yard box on Memphis Depay, who had hooked an Angel Correa cross from the right to turn.
Moments later, Barella wasted another golden opportunity on the counter-attack sparked by Lautaro Martinez, firing at the goalkeeper.
Atletico Madrid could not have gone closer on 85 minutes, as Depay’s daisy-cutter from outside the area bounced off the inside of the near post.
It was a warning and the hosts took the lead on the night moments later, Depay springing the offside trap from Koke’s pass to turn Stefan de Vrij and drill low into the near bottom corner from 12 yards.
Atleti wanted to win it in regular time, Sommer behind a Correa effort, but with the last kick of the game Griezmann rolled across from the right for Riquelme to somehow balloon over the bar undisturbed.
It went to extra time instead, the first time Inter experienced this in the Champions League since beating Celtic on penalties in the 1972 semi-final.
Thuram missed another great chance, steering the free header wide from Yann Bisseck’s cross, while Sommer had to make the save when Riquelme rolled across for Depay’s flick from six yards.
Lautaro Martinez’s header from a corner grazed the upright and Thuram was substituted after risking VAR intervention for squeezing Savic in a delicate area.
Calhanoglu had two attempts charged down and fired a free kick over, while Davide Frattesi’s pull-back from the by-line was beyond Lautaro Martinez.
It went to penalties, with Jan Oblak making two saves in a row on Alexis Sanchez and Davy Klaassen, as Sommer denied Saul Niguez with an outstretched leg.
Lautaro Martinez had to score to keep it going, but ballooned over the bar.
