The former Sunderland man headed home in the latter stages to deny the Scot a win against his old club, as the hosts played the majority of the second half with ten men
Christian Benteke opened the scoring with a fine finish but the visitors were handed a lifeline when Joseph Bennett saw red after two fouls on his namesake Elliot. And, despite some last-ditch defending from Villa, the Canaries snuck a point as Turner nodded home late on.
Paul Lambert made three changes to the side which lost against Fulham but again kept faith in Benteke, leaving Darren Bent among the substitutes. The hosts were also without Richard Dunne and Gary Gardner, who remain sidelined through injury.
Norwich fielded an unchanged side from the one that defeated Arsenal, with Grant Holt leading the line for the Canaries.
With both sides having picked up just one win this season, the game started as expected, a packed midfield allowing for little space in the middle of the park.
The game's first chance fell to the home side on 8 minutes, though. A counterattack started by Marc Albrighton saw Brett Holman attempt a through ball to Benteke, the deflected pass came back to him, but his low drive was well saved by John Ruddy.
Both teams lacked quality in posession in the early stages but, with 17 minutes played, Norwich had a soft penalty claim turned down by referee Phil Dowd, as Elliott Bennett went down under a challenge from Ron Vlaar just inside the box.
And they were soon on the front foot again, as Holt controlled a flick-on and played the ball through for Wes Hoolahan, who timed his run perfectly. His first-time shot was well met by the onrushing Brad Guzan in the Villa goal.
But it was the hosts who took the lead against the run of play, with 25 minutes on the clock. The Norwich defence was drawn to Holman as he received the ball on the left; he crossed for an unmarked Benteke, whose turn and shot beat Ruddy from 10 yards.
The goal appeared to be a wake-up call for Norwich, and an excellent spell for the visitors ended in a wild effort from Holt, but they went into the break trailing.
The second half started in similar fashion, but Villa were soon down to 10 men. Joe Bennett was shown a second yellow card for a needless tackle on Elliott Bennett, leaving his manager with little choice but to sacrifice Gabby Agbonlahor.
With an hour gone, there was another good chance for Hoolahan as he was put in on the left by Anthony Pilkington, but again Guzan rushed out to prevent a Norwich leveller.
Paul Lambert's side were struggling to break down the depleted Villa side, but were finally rewarded for their efforts with 10 minutes to go. A simple Hoolahan cross was headed in by Turner at the near post for a deserved equaliser.
Despite late pressure from the visitors, who looked the more likely throughout the second period, Villa held out for a point, to conclude a decent contest.