Manuel Pellegriniâ€™s men, who currently sit fourth in La Liga, moved through to the quarter-finals for the first time in the clubs history ahead of their four-year European ban which comes into play following this campaign.
Trailing 1-0 after the first leg in Portugal three weeks ago, Malaga made all the running in the first half only to have a goal disallowed late in the first half when Javier Saviola slotted home into an open goal but Julio Baptista had been penalised for a foul on goalkeeper Helton despite being pushed by defender Danilo.
Nevertheless, the home side took the lead in fine fashion in the 43rd minute when the super impressive Isco found space just outside the area before whipping an unstoppable shot from the right side of the box over Heltonâ€™s right shoulder and into the back of the net.
Disaster struck for Porto four minutes into the second half when Belgian midfielder Steven Defour was sent off for a second yellow card as Malaga looked to take complete control of the extra man advantage.
With just over 10 minutes remaining, substitute Roque Santa Cruz produced a meaningful first proper touch when he got his head on Iscoâ€™s outswinging corner to send Malaga into the lad.
It almost came back to bite them, however, as Porto had the ball in the back of the net in the 81st minute but Maicon has been adjudged offside as the Spaniards held on for a famous victory that sees them join fellow Spaniards Barcelona and Real Madrid in the final eight of Europeâ€™s premier club competition.
2012/13 UEFA Champions League â€“ Round of 16 second leg
La Rosaleda, Malaga â€“ 27,451
Red card: POR - Steven Defour 49â€™