Sadio Mane scored a hat trick and Mohamed Salah and Roberto Firmino provided the other two goals to give the Premier League side a huge advantage ahead of the second leg at Anfield on March 6.
Liverpool is the top-scoring side in the competition with 28 goals.
A mistake from Porto goalkeeper Jose Sa allowed Mane’s shot to squirm under his body after a slow start from the visitors, and Salah displayed all his class to make it 2-0 four minutes later inside the first half-hour.
James Milner hit the post but Salah was well-placed to take the rebound, lift it with his left foot and then head it past Sa before slotting into the empty net without letting it touch the ground.
It was the African player of the year’s sixth goal in the competition, and his ninth in eight games across all competitions.
The home side showed promise after the break but was caught on a counterattack when Sa saved Firmino’s effort, only to push the ball toward Mane’s feet. The Senegal striker needed no second invitation for his second goal.
Sa was playing in place of Iker Casillas, dropped earlier this season after falling out of favor with Porto coach Sergio Conceicao, who must have been reconsidering his decision after a shaky performance from the 24-year-old Sa.
At the other end, Virgil van Dijk marshaled Liverpool’s defence on his Champions League debut for the club following his winter switch from Southampton.
Firmino got the goal his performance deserved with a simple finish inside the left post from Milner’s cross with 20 minutes remaining, and Mane took advantage of some lax defending to seal the win with a fine strike from distance late on.