The Turkey international provided the finish to a fine free kick routine in the 86th minute to see the Spanish side come back from behind to see off the Portuguese champions
The Portuguese champions found it difficult to get through their visitors’ defence for much of the evening, but Jackson Martinez did gave them a 16th-minute lead with an excellent header.
Chelsea were the last side to defeat Porto at Estadio Dragao in November 2009 and that run came to an end in the second half thanks to Diego Godin and Turan.
Atletico followed up their first league victory over Real Madrid since 1999 at the weekend and Diego Simeone unsurprisingly made few changes.
Koke and the suspended Diego Costa came out of the starting XI, with Raul Garcia and Leo Baptistao taking their respective places.
The first 15 minutes saw Porto struggle to break Atletico down in open play, but all Paulo Fonseca’s side needed was a free-kick, and in the 16th minute they got their breakthrough.
Tiago fouled Josue on the left and the 23-year-old curled an inviting delivery into the area which Martinez knocked past Thibaut Courtois with a diving header, holding off Godin in the process.
Atletico's best opportunity of the half came in the final five minutes when Porto goalkeeper Helton flapped at Gabi's corner and pushed the ball onto the crossbar.
Simeone’s team looked significantly more motivated at the beginning of the second period and eight minutes in Luis Filipe narrowly missed the target with a shot from 30 yards.
After their encouraging start, Atletico equalised in the 58th minute as Godin atoned for his role in Martinez’s opener.
The Uruguayan rose highest to nod Gabi’s free kick past Helton, who needlessly rushed out in an attempt to punch the initial delivery away.
A few seconds after replacing Lucho Gonzalez, Juan Fernando Quintero fired a free-kick just past Courtois’ left-hand post as Fonseca looked to make his side more dynamic in attack.
Helton denied Garcia in the 76th minute, but he could not nothing to prevent Turan with just four minutes of normal time remaining.
A neat free kick routine saw Gabi pass through the Porto wall and the Turkey international smashed his effort past Helton from close range, completing Atletico's first away win against Portuguese opposition in eight attempts.