Porto started well and claimed a deserved lead through
Jackson Martinez's early header but Atletico improved after the break and
Diego Godin drew it level near the hour mark before Turkey international Turan slotted home an 86th-minute winner.
The 2-1 success leaves
Diego Simeone's side with six points from its 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 is still unbeaten in all competitions with nine wins from 11 games and claimed last weekend claimed its first victory over arch-rival 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 was 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.
Thibaut Courtois kept out a
Silvestre Varela shot during a strong Porto start but he was powerless to prevent Martinez giving the host 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 it hit the woodwork from a Gabi corner, but two minutes later it survived a let-off of its own when Varela's well-struck effort was saved by Courtois's feet.
Porto deserved that half-time advantage but Atletico came out positively after the break and was 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 which 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 its Iberian rival.