Davide Frattesi fired Inter Milan into the Champions League final with an extra-time winner which gave the Italians a stunning 4-3 triumph over Barcelona, 7-6 on aggregate.

Italy midfielder Frattesi won a tie for the ages under a downpour in Milan when he lashed home in the 99th minute, sending a packed and rocking San Siro wild with joy.

Simone Inzaghi's team will face either Arsenal or Paris Saint-Germain at the end of this month in Munich, where they will feel they have a great chance to be crowned kings of Europe for a fourth time after coming out on top in an epic contest.

Tuesday's triumph saved Inter's season as their bid for the treble went up in smoke after getting past Bayern Munich in the quarter-finals.

"It's just incredible, I don't know what to say. I thought after the Bayern game I couldn't ever feel the same emotions, but tonight was even more incredible," said Frattesi.

"This has been my career, really," he added. "I wasn't blessed with incredible talent, but I never give up and always believe and this is the reward for all my effort and dedication."

Inter conceded top spot in Serie A to Napoli, who are favourites to claim the domestic league title, after getting past Bayern while AC Milan dumped them out of the Italian Cup a fortnight ago.

But Inter ended Barca's hopes for the quadruple and now head into the final weeks of the season buoyant with a second Champions League final in three seasons to look forward to.

"We know that there are two really strong teams in the other semi. But you have to play to win any final," said Federico Dimarco.

Barca now have to try to maintain their four-point lead over Real Madrid at the top of La Liga on Sunday after missing out on a chance to claim every trophy available this season.

"The truth is we are sad. We wanted to get to the final, we were having a great Champions League campaign," said Ronald Araujo. "We were very close and it got away from us."

Frattesi's winning goal, his seventh of the season and probably the most important of his career, was all the more incredible for the fact that Inter should by rights have already been eliminated.

The hosts were heading out with two minutes remaining of regular time when Raphinha completed a comeback from two goals down at half-time and gave Barca a 3-2 lead on the night.

But Francesco Acerbi stunned everyone in the stadium, not least the already-celebrating Barca supporters, when he forced home Denzel Dumfries' cross in the second minute of added time.

That goal came as a bolt from the blue as Barca had been by far the better team in the second half of normal time after going in at the break behind to a brilliant Lautaro Martinez goal and Hakan Calhanoglu's penalty in first half stoppage-time.

Eric Garcia and Dani Olmo pulled Barca level with goals in the 54th and 60th minutes, both from sumptuous Gerard Martin deliveries, and Yann Sommer had to be at his best to keep Inter within touching distance.

Sommer made possibly the save of the season between Barca's first two goals, somehow stopping Eric Garcia from finishing off a lightning Barca counter-attack.

And the Swiss ended up being crucial again in the 113th minute when he pulled off another miraculous save from Lamine Yamal, who hit the post just before Acerbi's equaliser.

Inter then held off Barca as the home fans held their breath before unleashing a mighty roar at the final whistle of the match of the season. (AFP)