Both teams came into the second leg with an equal chance of progressing, after it ended 3-3 in Spain last Wednesday.
Inter Milan yesterday night defeated Barcelona in a thrilling encounter to qualify for the Champions League Final.
The match ended 4-3 in favour of Inter Milan.
The Serie A champions needed extra time to win the tie over two legs.
Both teams came into the second leg with an equal chance of progressing, after it ended 3-3 in Spain last Wednesday.
Inter reached their second Champions League final in three years by beating Barcelona in the most extraordinary of circumstances, with Simone Inzaghi’s side beating the Blaugrana 4-3 in Tuesday’s second leg at San Siro to progress 7-6 on aggregate.
As in the two teams’ first meeting at Montjuic, Inter went 2-0 up, with Lautaro Martinez breaking the deadlock before Hakan Calhanoglou doubled the hosts’ advantage with a penalty just before the break.
It was Barca, though, who looked certain to go through after second-half goals from Eric Garcia, Dani Olmo and Raphinha.
However, Inter threw Francesco Acerbi up front for the final few minutes and their 37-year-old centre-back netted a stunning injury-time equaliser.
Davide Frattesi then put the Nerazzurri back ahead with his fine finish in the first half of extra-time and Inzaghi’s men somehow hung on to claim victory in arguably the greatest Champions League semi-final tie every played.