The Portuguese side, who along with Chelsea are the only unbeaten teams in this season's competition, took the lead with an excellent first-half free kick from Yacine Brahimi, which set the tone for an evening of superb long-range efforts.
His opener was followed by equally impressive second-half strikes from Hector Herrera, Casemiro and Vincent Aboubakar with all four of the goals coming from outside the penalty area.
Porto were without their top scorer Jackson Martinez, but the Colombian's replacement, Cameroonian Aboubakar had an excellent game, causing Walter Samuel and Fabian Schaer in the Basel rearguard endless trouble.
After a period of early pressure, Basel were pegged back and the opening goal of a frenetic first half came after just 14 minutes.
Casemiro made a clean tackle to win the ball in the attacking third, putting Cristian Tello through on goal. He was up-ended on the edge of the box by Samuel and from the resulting free kick, Brahimi knocked an arching ball past Basel keeper Tomas Vaclik into the goal.
With Porto beginning to get up a head of steam, the match was broken up by a serious injury to the hosts' captain Danilo, who was flattened by his own keeper Fabiano, as the Brazilian came to head a long ball away.
He was substituted in the 22nd minute and taken to hospital where it was later confirmed that he had not suffered any serious injury.
Herrera made it 2-0 two minutes after the restart with a fine right-footed finish past Vaclik, as Porto took complete control of the tie.
Nine minutes later Casemiro scored what seemed to be the goal of the night with a stunning 35-metre free kick that left the keeper with no chance.
Yet even better was to come as stand-in striker Aboubakar capped an amazing second half by running from midfield and rifling home another wonderful goal to leave Basel out for the count.
"We started the game at full tempo, knowing that we had to be 100 percent emotionally, 100 percent concentrated and 100 percent balanced," said Mexico's Herrera.
"We are not thinking of the quarter-finals. We are thinking about reaching the final itself."
On this showing, Porto will be a handful for any of the sides going into the draw and will hope to have Martinez back in the side, after he was ruled out with a groin injury.
(Editing by Toby Davis)
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