Mohamed Salah and Roberto Firmino each scored twice, with Sadio Mane also finding the net as the Reds ran rampant over the Serie A side, leaving the Anfield outfit with three players on eight or more goals in the competition.
It marks the first time any club has had three players reach that mark in a single Champions League campaign, with S alah's fantastic double helping him set a Liverpool record along the way .
A 5-0 scoreline early in the second half had the Reds on the verge of another record. That mark would have been the largest margin of victory in a single Champions League semi-final match, topping Bayern Munich's 4-0 victory over Barcelona in 2013, and Real Madrid's 4-0 thumping of Bayern a year later.
But Roma had other plans and stormed back with two late goals of their own, leaving Liverpool with a three-goal advantage heading into the second leg in Rome.
Roma famously overcame a similar deficit to reach the semi-final stage, having taken down Lionel Messi and Barcelona 3-0 at the Stadio Olimpico after falling 4-1 to the Catalans in the first leg in Spain.
Liverpool will be wary in the second leg next Wednesday, knowing that another 3-0 win would see Roma pull off another stunning comeback.