The Reds looked set for a goalless draw in the first leg in Italy until Brazil forward Roberto Firmino got on the end of Andrew Robertson’s corner to head his side into the lead.
Mohamed Salah added a double with an effort seen from inside the box, meaning Jurgen Klopp’s side got a pretty big advantage in the second leg at Anfield on 8 March.
Italian champions Inter attacked the bar through Hakan Calhanoglu and were on top for a long time in the second half before Firmino struck in the 75th minute.
Liverpool scored from just two attempts for the target and will be a strong favorite to move forward when the two meet in the deciding leg next month.
This was a very important night for midfielder Harvey Elliott, who became the youngest player to start a match in competition for Liverpool at the age of 18 years 318 days.
The only negative on an optimistic night for the Reds was an injury to Portugal striker Diogo Jota, who was replaced by goalkeeper Firmino early in the second half after suffering an ankle injury.