Benfica had slightly more of the ball while both teams created seven shots on goal.
Nicolo Barella and Romelu Lukaku scored second-half goals at Lisbon's Stadium of Light to give Inter their first victory in more than a month.
Barella’s goal came just after half time, with the Italian getting on the end of a Bastoni cross and heading it across the goalkeeper into the far post.
Lukaku scored via a penalty in the 82nd minute, awarded by VAR for a handball.
Benfica’s Vlachodimos picked the right way, but couldn’t keep it out.
It leaves the Italian giants in a strong position to reach the semis of the European competition for the first time in more than a decade.
It was Benfica's first Champions League loss in 13 matches this season, having gone through the third qualifying round and on an unbeaten run to win a difficult group that included PSG and Juventus.
The return leg will be in Milan on Thursday, April 20 at 5am AEST.
AAP
