Roque Santa Cruz scored with his first touch to send Malaga into the quarter-finals of the Champions League.
Trailing 1-0 from the first leg, the Spanish side moved level on aggregate when Isco curled in the opener from the edge of the box just before half-time.
Porto's Steven Defour picked up a second yellow in the 50th minute for a cynical foul on winger Joaquin.
Then substitute Santa Cruz, on loan from Manchester City, powered in a 78th minute header from Isco's corner.
While the Paraguayan showed the killer instinct that convinced City to pay £18m for him in 2009, it was team-mate Isco, who was the star of the show.
Y Viva Espana
Malaga join Barcelona and Real Madrid in the quarter-finals - the first time three Spanish sides have reached the last eight in 10 years.
The 20-year-old playmaker, who earned his first full cap for Spain in February, showed remarkable composure as the tension threatened to overcome the Champions League debutants.
With the game finely poised following Porto's narrow lead in the first leg last month, both sides seemed more determined not to concede the crucial opening goal.
In a frenetic first half, there were more yellow cards that shots on target with a rash of cynical tackles disrupting the action.
But Isco provided a rare moment of quality to change the tie just before the break. He turned neatly on the edge of the box before curling a delicious shot over the stranded goalkeeper Helton.
Argentine striker Javier Saviola had found the back of the net five minutes earlier for Malaga but his effort was controversially ruled out.
Helton spilled the ball under a challenge from Julio Baptista but the Brazilian forward looked like he had been pushed into the keeper by Porto defender Danilo.
Porto's hopes were not helped at half-time when influential playmaker Joao Moutinho was forced off with a troublesome thigh injury.
And they made their job even harder four minutes after the restart when Defour picked up a second yellow card for stupidly tripping Joaquin as the winger glided past him.
The visitors retreated to the edge of the box as Isco and team-mates Manuel Iturra and Joaquin teased and probed although Malaga struggled to create any clear-cut chances.
That was until they were finally ahead for the first time in the tie in the 78th minute as Santa Cruz rose highest to head home Isco's outswinging corner.
Porto almost snatched a tie-winning away goal two minutes later when substitute Maicon headed in James Rodriguez's free-kick but the Brazilian defender was marginally offside.
Malaga midfielder Isco:
"An achievement like this seemed impossible only a short time ago. It is a dream for everyone here.
"We came out of the blocks with a lot of intensity because that is what this tie demanded of us. We then settled into the match and showed what we were capable of.
"I think we deserved the win. We enjoyed ourselves and we played in such a way that our fans enjoyed the game too.
"The Champions League is the essence of football and we will continue to enjoy it no matter where it takes us next."
Porto coach Vítor Pereira:
"We are sad with the exit and we understand that the supporters are sad. We are all sad.
"Steven Defour's sending off and Joao Moutinho's injury influenced the match. We tried to react even with ten men and control the game.
"Every event in the game made our life difficult."
Live Text Commentary
Full Time The final whistle is blown by the referee.90:00 +3:26
Martin Demichelis concedes a free kick for a foul on Jackson Martinez. Eliaquim Mangala takes the free kick.90:00 +1:41
James Rodriguez takes a shot. Caballero Willy makes a comfortable save.90:00 +1:01
Alarcon Isco takes a shot. Save by Da Silva Danilo.88:41
The referee blows for offside against Jackson Martinez. Caballero Willy takes the free kick.87:41
Free kick awarded for a foul by Nacho Camacho on James Rodriguez. James Rodriguez restarts play with the free kick.87:05 Substitution
Substitution Nacho Camacho joins the action as a substitute, replacing Sanchez Joaquin.85:28
Inswinging corner taken right-footed by Alarcon Isco from the left by-line to the near post, save by Da Silva Helton.82:56
Sanchez Joaquin crosses the ball in from the free kick, save by Da Silva Helton.82:56 Booking
Booking Eliaquim Mangala receives a caution for unsporting behaviour.82:40
Free kick awarded for a foul by Eliaquim Mangala on Duarte Jesus Gamez.81:58
Christian Atsu takes a shot. Blocked by Oliveira Weligton.81:23
The assistant referee flags for offside against Roque Santa Cruz. Direct free kick taken by Da Silva Helton.79:25
The ball is swung over by Da Silva Danilo, save by Caballero Willy. Manuel Iturra concedes a free kick for a foul on Da Silva Danilo. Free kick crossed left-footed by James Rodriguez. Roque Maicon is flagged offside by the assistant referee. Caballero Willy takes the direct free kick.76:41 Substitution
Substitution Javier Saviola goes off and Lucas Piazon comes on.76:41
Assist by Alarcon Isco.76:41 Goal scored
Goal! - Roque Santa Cruz - Malaga 2 - 0 FC Porto Roque Santa Cruz grabs a headed goal from inside the area. Malaga 2 (2)-(1) 0 FC Porto.76:30
Outswinging corner taken by Alarcon Isco from the right by-line,76:06
Inswinging corner taken by Sanchez Joaquin, Da Silva Danilo manages to make a clearance.73:42
Jeremy Toulalan challenges Jackson Martinez unfairly and gives away a free kick. The ball is delivered by James Rodriguez, Shot by Jackson Martinez from deep inside the penalty area misses wide to the left of the target.
Substitution Roque Santa Cruz joins the action as a substitute, replacing Cesar Julio Baptista.70:19
Nicolas Otamendi fouled by Manuel Iturra, the ref awards a free kick. Direct free kick taken by Nicolas Otamendi.68:41
Jeremy Toulalan takes the free kick.68:41 Substitution
Substitution Christian Atsu replaces Lobo Alex Sandro.68:41
Free kick awarded for an unfair challenge on Sanchez Joaquin by Jackson Martinez.66:06
Corner taken right-footed by Sanchez Joaquin.63:27
Free kick taken by Roque Maicon.63:27 Booking
Booking Jeremy Toulalan goes into the referee's book for unsporting behaviour.63:24
Free kick awarded for a foul by Jeremy Toulalan on Lucho Gonzalez.61:45
Effort from inside the six-yard box by Alarcon Isco goes wide right of the target.59:35
The ball is delivered by Javier Saviola, Da Silva Danilo manages to make a clearance.58:47
Corner taken by Alarcon Isco from the left by-line, Eliaquim Mangala makes a clearance.57:27
Corner taken by Sanchez Joaquin, Alarcon Isco takes a shot from just inside the penalty box which clears the crossbar.57:27 Substitution
Substitution (FC Porto) makes a substitution, with Roque Maicon coming on for Silvestre Varela.57:00
Javier Saviola takes a shot. Blocked by Nicolas Otamendi.56:14
The ball is swung over by Duarte Jesus Gamez, Eliaquim Mangala manages to make a clearance.54:12
Free kick awarded for a foul by Oliveira Weligton on Jackson Martinez. Da Silva Danilo takes the direct free kick.53:26
Duarte Jesus Gamez crosses the ball, save by Da Silva Helton.48:35
Sanchez Joaquin takes the free kick.48:35 Dismissal
Dismissal Steven Defour sent from the field by the ref for second bookable offence.48:28
Free kick awarded for a foul by Steven Defour on Sanchez Joaquin.47:44
Alarcon Isco concedes a free kick for a foul on James Rodriguez. Free kick taken by James Rodriguez.47:14
The offside flag is raised against Javier Saviola. Da Silva Helton takes the indirect free kick.45:36
Foul by James Rodriguez on Cesar Julio Baptista, free kick awarded. Free kick taken by Jeremy Toulalan.45:01
The match restarts for the second half.45:01 Substitution
Substitution James Rodriguez comes on in place of Felipe Joao Moutinho.45:00 +0:11 Half time
Half Time The players leave the pitch at half time.42:28
Assist by Manuel Iturra.42:28 Goal scored
Goal! - Alarcon Isco - Malaga 1 - 0 FC Porto Goal scored by Alarcon Isco from just outside the penalty area to the top left corner of the goal. Malaga 1 (1)-(1) 0 FC Porto.41:11
Sanchez Joaquin produces a cross, clearance made by Nicolas Otamendi.40:20
Silvestre Varela concedes a free kick for a foul on Vitorino Antunes. Free kick taken by Vitorino Antunes.40:03
Foul by Cesar Julio Baptista on Da Silva Helton, free kick awarded. Direct free kick taken by Da Silva Helton.39:16
A cross is delivered by Duarte Jesus Gamez, Da Silva Helton makes a save.38:50
Jackson Martinez concedes a free kick for a foul on Jeremy Toulalan. Duarte Jesus Gamez takes the free kick.38:13
Jeremy Toulalan challenges Silvestre Varela unfairly and gives away a free kick. Silvestre Varela takes the free kick.36:43
The offside flag is raised against Javier Saviola. Da Silva Danilo takes the free kick.34:50
Outswinging corner taken from the right by-line by Sanchez Joaquin, clearance by Francisco Fernando. Vitorino Antunes takes a shot. Da Silva Helton makes a save. Corner taken by Sanchez Joaquin.33:40
Centre by Silvestre Varela.32:13
Free kick crossed by Felipe Joao Moutinho, clearance by Vitorino Antunes.32:13 Booking
Booking Duarte Jesus Gamez goes into the book for unsporting behaviour.32:08
Free kick awarded for an unfair challenge on Lobo Alex Sandro by Duarte Jesus Gamez.31:15
The ball is swung over by Jeremy Toulalan.30:13
Effort on goal by Sanchez Joaquin from inside the penalty area goes harmlessly over the bar.29:30
Direct free kick taken by Jeremy Toulalan.29:30 Booking
Booking Lobo Alex Sandro receives a caution.29:18
Free kick awarded for an unfair challenge on Javier Saviola by Lobo Alex Sandro.27:55
Felipe Joao Moutinho takes the direct free kick.27:55 Booking
Booking Martin Demichelis goes into the referee's book.27:47
Unfair challenge on Jackson Martinez by Martin Demichelis results in a free kick.26:22
Steven Defour takes a shot from inside the box clearing the bar.25:56
The referee blows for offside. Eliaquim Mangala takes the direct free kick.25:17
Manuel Iturra challenges Lucho Gonzalez unfairly and gives away a free kick. Direct free kick taken by Nicolas Otamendi.24:10
Oliveira Weligton takes the direct free kick.24:10 Booking
Booking Booking for Steven Defour.23:50
Unfair challenge on Alarcon Isco by Steven Defour results in a free kick.23:37
Outswinging corner taken by Felipe Joao Moutinho from the right by-line played to the near post.23:06
Effort on goal by Lucho Gonzalez from just outside the area goes harmlessly over the target.22:28
Manuel Iturra fouled by Steven Defour, the ref awards a free kick. Vitorino Antunes takes the free kick.21:57
Manuel Iturra concedes a free kick for a foul on Jackson Martinez. Lucho Gonzalez takes the free kick.20:31
Unfair challenge on Martin Demichelis by Jackson Martinez results in a free kick. Martin Demichelis restarts play with the free kick.18:50
Felipe Joao Moutinho takes the outswinging corner, clearance by Sanchez Joaquin.16:44
Direct free kick taken by Alarcon Isco.16:44 Booking
Booking Nicolas Otamendi goes into the referee's book for unsporting behaviour.16:34
Vitorino Antunes fouled by Nicolas Otamendi, the ref awards a free kick.16:09
Lobo Alex Sandro gives away a free kick for an unfair challenge on Javier Saviola. Free kick taken by Jeremy Toulalan.12:45
Jackson Martinez challenges Manuel Iturra unfairly and gives away a free kick. Free kick taken by Martin Demichelis.11:38
Foul by Eliaquim Mangala on Cesar Julio Baptista, free kick awarded. The ball is swung over by Alarcon Isco, Cesar Julio Baptista takes has a header from just inside the penalty box which clears the crossbar.10:41
Steven Defour challenges Martin Demichelis unfairly and gives away a free kick. Caballero Willy takes the free kick.8:46
Close range shot by Da Silva Danilo clears the bar.6:38
Free kick awarded for a foul by Manuel Iturra on Lucho Gonzalez. Lucho Gonzalez takes the free kick.6:01
The assistant referee signals for offside against Jackson Martinez. Direct free kick taken by Caballero Willy.0:57
The referee blows for offside against Sanchez Joaquin. Lobo Alex Sandro takes the free kick.0:00
The referee gets the match started.
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