The Portuguese champions could have been forgiven for taking their foot off the gas after hammering Spartak in the first leg, but continued where they left off and killed the tie off in Moscow.
The five Porto goals came from five different players with Hulk, Cristian Rodriguez, Fredy Guarin, Falcao and Ruben Micael all scoring. Artem Dzjuba and Ferreira Ari grabbed consolation goals for the hosts.
Spartak started the game brightly but could not find a way through the Porto defence although Aiden McGeady was a constant source of trouble on the right flank in the first half and cut inside before forcing a great save from Helton after seven minutes.
Hulk opened the scoring after 28 minutes as he caught the home defence pushing up to the halfway line and took the ball by himself, outpacing the chasing pack before slotting passed Andrei Dikan in the Spartak goal from 12 yards.
Joao Moutinho then fired just wide as Porto began to take control of the game, but only seconds later Spartak forward Pavel Yakovlev fired over from the edge of the six-yard box when he should have done much better.
Alex then beat Porto's offside trap but could not keep his shot down after being pressurised into an early shot by Alvaro Pereira .
Then on the stroke of half-time Dikan turned a 25-yard volley from Hulk around the post before the Brazilian delivered the resulting corner to the near post for Rodriguez to head home Porto's second.
There was then a flurry of goals at the start of the second half.
Guarin benefited from some great work from Falcao in the 47th minute as the Europa League's top goalscorer forced a smart save from Dikan before turning the rebound into the path of Guarin, whose cool finish put the tie firmly out of Spartak's reach.
The home side managed to pull a goal back five minutes later as Dzjuba produced a couple of pieces of individual skill to beat two defenders before sidefooting past Helton.
Not to be outdone Porto needed only two minutes to re-establish their three-goal lead on the night as Falcao converted with a diving header from six yards after a corner was flicked into his path.
The pace of the game inevitably dropped after the hectic start to the second half, but Spartak still managed to reduce the arrears on the night to 4-2 after 71 minutes when substitute Ari used his strength to hold off Jorge Rolando before rounding Helton and sliding home.
Porto then reached double figures over the two legs in the 89th minute when a missed clearance allowed Hulk to fire in a shot which cannoned back off the crossbar and into the path of substitute Micael, who made no mistake.
Spartak Moscow 2-5 FC Porto: Match Report - view commentary, squad, and statictics of the game as it happened.