The former Sunderland man headed home in the late stages to deny Paul Lambert a win against his previous employer, as Villa played most of the second half with 10 men.
Villa boss Paul Lambert made three changes to the side that lost against Fulham, and again kept faith in Christian Benteke, leaving Darren Bent among the substitutes. The home side was 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. Turner and Sebastien Bassong again formed the central defensive partnership for the visitors.
With both sides having picked up just one win prior to kickoff, 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 eight minutes. A counter attack 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 possession 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 the strength of Ron Vlarr just inside the box.
The team was 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 home side which took the lead against the run of play with 25 minutes on the clock. The Norwich defense 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 team ended in a wild effort from Holt, and the visiting side went into the break trailing.
The second half started in similar fashion, but Villa was soon down to 10 men. Joe Bennett was shown a second yellow card for a needless tackle on namesake Elliott Bennett, leaving his manager 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 leveler.
Paul Lambert's side was struggling to break down the depleted Villa side, but was finally rewarded for its efforts with 10 minutes to go. A simple Hoolahan cross was headed in by Turner at the near post for a deserved equalizer.
Despite late pressure from Norwich, which looked the more likely throughout the second period, Villa held out for a point to conclude a decent contest at Villa Park.
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