The Italian side raced into a two-goal lead with superb strikes from Marcus Thuram and Denzel Dumfries, before the unstoppable Lamine Yamal pulled Barca back into it with a sublime solo effort.
Ferran Torres levelled for the five-time champions and although Inter nosed ahead through Dumfries again, a Yann Sommer own goal left the tie on a knife-edge at the halfway stage.
Inter were desperately hoping Thuram would be fit to play after a thigh injury and he showed precisely why, scoring the fastest ever Champions League semi-final goal after 30 seconds.
Barcelona’s Copa del Rey final winning goalscorer Jules Kounde hacked a poor clearance to the edge of the box, and Inter capitalised.
Dutch wide man Dumfries aimed a low cross towards Thuram and Inigo Martinez slipped at just the wrong time, allowing the France striker room to finish with an impudent back-heel flick.
Quadruple-chasing Barcelona seized control and pushed forward, roared on by a nervous 50,000 strong Olympic stadium crowd.
Yamal, on his 100th Barcelona appearance, appealed for a penalty after he was shoved by Alessandro Bastoni and then set up Torres, who fired wide.
The Spaniard, standing in for Barca’s injured top goalscorer Robert Lewandowski, lashed a volley narrowly off target.
Against the run of play Inter, whose treble hopes crumbled after three consecutive domestic defeats prior, scored their second, with another fine finish.
Francesco Acerbi nodded on a corner and Dumfries reached the dropping ball first to score with a stunning acrobatic effort.
Barcelona teams over the past few years may have crumbled but Hansi Flick’s youthful side are not burdened by the series of European failures since they last won the competition in 2015.
Least of all teenage wizard Yamal, who pulled Barcelona back into the game just three minutes later with a wonderful individual goal that made him the youngest player ever to score in the semis.
On the eve of the game the Spaniard rejected comparisons to all-time Barca great Lionel Messi, but his goal was straight from the Argentine’s playbook.
Yamal shook off Thuram, floated inside from the right flank and past Henrikh Mkhitaryan into the box, drawing defenders towards him but before they could stop him, stroked an inch-perfect shot in off the left post.
Minutes later, Yamal nearly repeated the trick. This time he darted outside, pausing to let Federico Dimarco lunge past him and off the pitch.
From a tight angle the youngster flashed a shot that Sommer tipped onto the crossbar.
High on confidence Yamal set up further chances for Torres and Dani Olmo that went begging, before Barca pulled level.
Pedri hooked a ball into the area for Raphinha to head across goal and Torres to convert from close range after 38 breathless minutes.
Kounde limped off before half-time in a blow for Barca, who also replaced the inexperienced Gerard Martin with Ronald Araujo at the break.
Dimarco hammered over early in the second half before Simone Inzaghi hooked him, after a torrid night up against the relentless Yamal.
Inter took the sting out of the game early in the second half and then sucker-punched Barca, scoring from another corner, with Dumfries’ header bouncing in off Olmo.
Barcelona equalised within two minutes, with Yamal stepping over a corner on the edge of the box, allowing it to run to Raphinha.
The Brazilian’s rasping effort smashed against the crossbar and then in, off the back of the unfortunate diving Sommer’s head.
Pau Cubarsi made a vital recovery tackle to stop Thuram after he got in behind Barcelona’s high line, and Mkhitaryan had a goal ruled out for an extremely tight offside.
Yamal looped a second strike onto the crossbar late on, but the sides could not be separated.
The second leg takes place in Milan next Tuesday, with the winner to face Paris Saint-Germain or Arsenal on May 31 in the Munich final. (AFP)
