The Champions League debutants' achievement is remarkable given their chaotic close-season when several top players were sold and their financial difficulties eventually earned them a ban from future UEFA competition for at least a season.
Porto, the 2004 winners, started strongly at a packed and vibrant Rosaleda before Malaga's highly-rated playmaker Isco, the standout performer on the night, put the home side ahead with a brilliant curling effort two minutes before half-time.
Porto's hopes were dealt a further blow four minutes after the break when midfielder Steven Defour was shown a second yellow card and sent off for a late tackle on Joaquin.
With a numerical advantage and the crowd whipping them on, Malaga probed patiently for a second and Roque Santa Cruz headed into the net from Isco's corner in the 77th minute, moments after coming off the bench.
The tie was still delicately balanced and Porto threw men forward but Malaga held firm to ensure their name will be included in Friday's draw for the quarter-finals along with Barcelona, Real Madrid, Bayern Munich, Borussia Dortmund, Juventus, Paris Saint-Germain and Galatasaray.
"We played a poor first leg away but we are back in the best possible way," Isco said in an interview with Spanish television broadcaster Canal Plus.
"This would have been unthinkable only a short time ago, it's incredible," added the 20-year-old, struggling to make himself heard over the noise of the home fans celebrating up in the stands.
"Nobody here has ever experienced anything like this and they all deserve it.
"We started with a lot of tension but later we realised we were capable of doing something and I think we fully deserved the win. We enjoyed the match and we played our football."
ACROBATIC SAVE
Leading 1-0 from last month's game in Portugal, Porto dominated the early stages but had to wait until the ninth minute before creating their first genuine chance when Danilo fired an angled shot over the bar.
Malaga gradually gained a measure of control and began to threaten going forward and Porto goalkeeper Helton was forced into an acrobatic save to deny Antunes in the 35th minute.
A moment of brilliance from Isco finally broke the deadlock two minutes before half-time.
He picked up the ball outside the area, moved into space and curled a superb shot over Helton into the top-left corner.
He came close to a second from a tight angle just after the hour before providing the assist for Santa Cruz's decisive goal on a superb night for the Spain Under-21 international.
Porto coach Vitor Pereira said his side's chances had been dented by an injury to Joao Moutinho that forced the influential midfielder, who scored his side's goal in the first leg, off at the break.
"The game was balanced until the middle of the first half but then Moutinho started feeling an injury and we had to substitute him at half-time," Pereira told Portuguese television.
