Atlético took an early lead with goals from Julián Álvarez in the first minute and Antoine Griezmann in the sixth, but the home side had levelled the game by the 21st minute thanks to two goals two minutes apart from Pedri and Pau Cubarsí.
Hakan Calhanoglu sealed the win for Inter in the 77th minute from the penalty spot, sending the Lazio goalkeeper, Christos Mandas, the wrong way after Samuel Gigot fouled a charging Joaquín Correa.
The home side, who have now eliminated three Bundesliga clubs in a row after wins over Union Berlin and Freiburg in the previous rounds, went in front after Werder lost possession in their own half and Marius Wörl curled in a shot after 35 minutes.
The second leg will be at Atlético’s Metropolitano Stadium will be in April and the winner will play either Real Madrid or Real Sociedad, who will play the first leg of their tie on Wednesday.
The visitors pulled closer through Marcos Llorente in the 84th minute and Alexander Sørloth got the equaliser from close range in the third minute of stoppage time.
