Sadio Mane acrobatically fired an effort over the bar and hit the post in a generally tame first half that also saw Dejan Lovren head narrowly wide.
Majeed Waris’ strike in the second half was Porto’s only shot on target.
The Reds took a 5-0 lead into the game.
It was always likely this might be a quiet affair with Liverpool having already done the damage in Portugal on Valentines Day.
Jurgen Klopp used the opportunity to rest players for Liverpool’s Premier League match against Manchester United on Saturday (12:30 GMT), making five changes to the starting line-up.
Virgil van Dijk and Mohamed Salah were named among the substitutes but the Egyptian did have a cameo in the second half as Mane was given a breather.
There was also a chance for Joe Gomez and Adam Lallana to gain further fitness following returns from injury – while Danny Ings enjoyed some rare game-time as a second-half substitute.
Liverpool will discover their quarter-final opponents when the draw is made on 16 March (11:00 GMT). The ties will be played in the first and second weeks of April.
It is almost 11 years since Liverpool faced AC Milan in the Champions League final, losing 2-1 in Athens.
Back then they were hitting the heights in European football pretty regularly – the most successful English club in the competition’s history, it was just two years since they had beaten the same opponents to lift their fifth trophy on a famous night in Istanbul.
But since being knocked out at the group stage in 2009, Liverpool have only featured in the Champions League twice.
It was a dejected-looking Reds side who trudged off the field in December 2014, a 1-1 draw with Basel confirming their elimination from the competition after a wretched campaign.
It would be Steven Gerrard’s last game in the Champions League – a Liverpool legend bowing out with a goal but unable to reproduce the heroics he had done against Olympiakos a decade before en route to Istanbul.
After five years of waiting, it wasn’t the way Liverpool had dreamt their comeback would go.
Four more years on, Liverpool are back. And this time they look more than worthy members of Europe’s elite.
They have cantered into the quarter-finals – barely hitting second gear – and now they eye the prize of a place in the last four.