Jurgen Klopp's team were in front just after 25 minutes when Sadio Mane curled a shot under Porto keeper Jose Sa for his first of three goal on the night.
And the visitors doubled the lead less than five minutes later when Mohamed Salah used some nifty footwork to evade Sa in front of goal after collecting a James Milner rebound and tap home to send Liverpool to the dressing room up 2-0.
Liverpool effectively killed off the tie in the second half when Mane tapped home a rebound from a Roberto Firmino shot and Firmino then first-timed a Milner pass into the back of the net to make it 4-0.
Mane then added his third and Liverpool's fifth, smashing an unstoppable shot from 20 yards away that left Sa no chance.
The five-goal outing puts Klopp's team atop the UCL team scoring charts with 28 strikes in the competition.
Porto will travel to Liverpool for the second leg at Anfield on March 6 needing nothing short of a miracle to overturn the first-leg deficit.