The Reds have had the wood over Porto in recent seasons and that run continued with a stunning win at the Estadio do Dragao.
Mohamed Salah's prodded finish after 18 minutes got Liverpool off to the perfect start and there was no looking back.
Sadio Mane extended their lead on the stroke of half-time with a back-post tap in before Salah got his second with 60 minutes on the clock.
Firmino rounded off the win four minutes later when he pounced on a rebound from Curtis Jones' volley.
With two wins from their opening two games, Liverpool have put themselves in a great position to qualify for the knockout stages.
But captain Jordan Henderson has warned his team not get complacent over the last four games.
"It's definitely not job done as we have four games to play," Henderson told reporters. "We had two good performances, applied ourselves well and got results we deserved. It's a good start but it is far from over.
"We'll be disappointed to concede as I thought we were dominant throughout the game. We scored some brilliant goals and played good football so we have got to be pleased as it is a difficult place to come."
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