The return match will be held next Tuesday at the Giuseppe Meazza Stadium to determine qualification for the final.
Inter took the lead through Marcus Thuram just 30 seconds into the match after a cross that Thuram skillfully redirected into the net with his heel, and in the 21st minute, Denzel Dumfries scored a second goal for Inter following a corner kick.
In the 24th minute, Barcelona scored their first goal through Lamine Yamal with a brilliant shot from inside the penalty area, then Ferran Torres scored a second goal in the 38th minute after a ball reached him from Raphinha.
In the 64th minute, Inter scored a third goal through Denzel Dumfries after a corner kick that Dumfries headed into the net, while Barcelona equalized after a shot from Raphinha hit the post, then hit Sommer and went into the net.
Inter scored a fourth goal through Mkhitaryan, but it was disallowed for offside after consulting the video technology in the 75th minute.
