Colin Cameron had given the visitors an early lead but late first half strikes from Mikael Forssell and Clinton Morrison gave Blues a 2-1 half time lead.
However, January signing Cort popped up with a quarter of an hour left to earn Wolves a point towards their fading Premiership survival hopes.
In sunny conditions at St Andrews, it was Wolves who started brightly with Henri Camara going close after a fine run and left-footed shot that skipped just past Maik Taylor's left-hand post.
The visitors continued to threaten in the early stages and it only took Wolves six minutes to go in front with a fine goal from Cameron.
The Scot played a give and go with Camara on the edge of Birmingham's box before hitting a right-footed curler past Taylor to make it 1-0 to the visitors.
Camara was a constant threat to Birmingham's back-line and he was presented with more opportunities to score himself, but poor finishing and Taylor prevented the Senegalese star from getting on the scoresheet.
The home side started to come into the match themselves and Stephen Clemence will wonder how he did not score midway through the opening period.
Stan Lazaridis's through ball to Clemence in Wolves' box saw him side-step his marker, but with the goal at his mercy, he agonisingly placed his shot wide.
Despite the missed chance, Steve Bruce's side continued to press forward and 11 minutes before the break, they drew level.
Matthew Upson's free kick from the halfway line flicked off Paul Ince's head before Morrison knocked it down to Forssell under pressure in the box.
The Finnish star eluded Wolves defender Isaac Okoronkwo before rounding Paul Jones and slipping the ball home for 1-1.
Birmingham looked the stronger side towards the break and they took a lead into half time when Forssell neatly turned and slipped a through ball to Morrison, who beat Wolves' offside trap.
The former Crystal Palace hit-man slipped the ball past the oncoming Jones to make it 2-1 to the home side.
Birmingham were unlucky not to further extend their lead before the break, as Robbie Savage curled a sublime right foot free kick over the Wolves wall before hitting the near post, with Jones sprawling to reach the set piece.
The second half saw the match continue to be a well-fought battle by both sides, but unlike the first half, goal opportunities were not as plenty.
At times, the match turned into a scrappy affair, with the away side keen to pull level and improve their Premiership survival hopes.
That much-needed equaliser soon came as Wolves were awarded an indirect free kick just outside Birmingham's box with a quarter of an hour to go.
Ince rolled the set piece into the path of Mark Kennedy and his rasping drive was not parried properly by Taylor and Cort was quickest to react and make it 2-2 to delight the travelling support behind the goal.
Birmingham soon replied with Savage again going close with another curling right foot free kick that was deflected away by a Wolves marker for a corner while substitute Stern John squandered an injury time effort right at Jones.
Both Birmingham and Wolves were forced to share the spoils in the end, with the result doing little to improve Blues' chances of getting into Europe and Wolves' hopes of staying in the top flight.
