The Gunners gave away two dreadful goals as they lost out in the Estadio do Dragao.
The home side made the brighter start, with Hulk shooting wide from 15 yards with just three minutes on the clock.
With 11 minutes played Arsenal fell behind as Silvestre Varela fired a low ball in from the right and Polish goalkeeper Lukasz Fabianski fumbled it into his own net from close to the goal-line.
Arsenal responded well to the setback and drew level seven minutes later after a Nicklas Bendtner drive from 20 yards was deflected narrowly wide of the far post.
From the resulting Cesc Fabregas corner, Tomas Rosicky headed the ball back from beyond the far post and Sol Campbell nodded home from a couple of yards out.
Soon after Rosicky forced Helton into a fine, diving save with a stinging 20-yard drive from the right edge of the area, while at the other end Fabianski had to turn away a 25-yard drive from Ruben Micael.
The first half ended with tempers being raised following a couple of late challenges on Fabregas.
Early in the second half Rosicky was denied a penalty when he appeared to be brought down in the area, before Porto grabbed the lead with another bizarre goal.
Campbell touched the ball back to Fabianski, who conceded a free-kick by handling the back-pass. Ruben Micael grabbed the loose ball and took the set-piece quickly, playing in Falcao to slot home as the Gunners defence failed to react.
The goal prompted Arsene Wenger to enter a long discussion with the referee, obviously unhappy that the free-kick was taken so quickly.
Arsenal were clearly affected by the goal and Fabianski had to make saves from Hulk and Raul Meireles as Porto took the upper hand.
The game then became bitty as a series of free-kicks and substitutions ruined the flow of play, with neither keeper seriously tested in the closing stages.
The closest the visitors came to an equaliser came in stoppage time as Emmanuel Eboue did superbly down the right and his cross was set to reach Fabregas, before Rolando made a vital interception.