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, AFP reported.
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.
"Letting in that many goals (here) is unacceptable, but we also have to give Inter credit, they did very well," said Raphinha, whose fierce drive forced the own goal.
"The important thing is we leave with a result where everything can happen."
Despite losing three domestic games in a row and seeing their treble hopes crumble, Inter showed resilience and quality in Catalonia, according to AFP.