Porto started well and claimed a deserved lead through Jackson Martinez's early header but Atletico improved after the break and Diego Godin drew them level near the hour mark before Turkey international Turan slotted home an 86th-minute winner.
The 2-1 success leaves Diego Simeone's men with six points from their two Group G games and is further proof that the Rojiblancos could be a force to be reckoned with both in Spain and Europe this season.
Atletico are still unbeaten in all competitions with nine wins from 11 games and on Saturday claimed their first victory over arch rivals Real Madrid since 1999 with a 1-0 triumph at the Bernabeu.
Diego Costa scored the only goal of that game to take his league tally to eight for the season, but Atletico were without him in Portugal as he served the second of a two-match European ban and it was Porto's own red-hot forward who made the early breakthrough on Tuesday.
Visiting goalkeeper Thibaut Courtois kept out a Silvestre Varela shot during a strong Porto start but he was powerless to prevent Martinez giving the hosts a 16th-minute lead.
The Colombia international escaped the attentions of his marker to nod in a diving header from Josue's free-kick to take his tally to six in league and Europe this term.
Martinez then set up Lucho Gonzalez for a shot that went just over as Porto sought a second, before Atletico finally started to pose an attacking threat 30 minutes in when Raul Garcia and Turan went close in quick succession.
The Spanish side then came within a whisker of drawing level in the 41st minute when they hit the woodwork from a Gabi corner, but two minutes later they survived a let-off of their own when Varela's well-struck effort was saved by Courtois' feet.
Porto deserved that half-time advantage but Atletico came out positively after the break and were rewarded with an equaliser in the 58th minute when Godin beat two defenders and home goalkeeper Helton to power home Gabi's free-kick.
Both sides pushed for a winner after that with Porto substitute Quintero firing just wide and Helton doing superbly to tip behind Garcia's shot, but it was Atletico who would find the decisive breakthrough as Turan's close-range finish from Gabi's clever free-kick inflicted a first defeat of the season on their Iberian rivals.