Christian Benteke justified Lambert's decision to axe Darren Bent from his starting line-up for the third time in four matches with Villa's 27th-minute opener.
But Villa were forced to defend desperately after left-back Joe Bennett's sending-off early in the second period before Turner earned the Canaries a deserved share of the spoils.
Norwich, fresh from last weekend's win over Arsenal, knocked the ball around in confident fashion in the early stages but it was Villa midfielder Brett Holman who produced the first attempt on goal. He exchanged passes with Karim El Ahmadi before firing a low drive which Canaries keeper John Ruddy got his body behind.
It needed a fine save by Brad Guzan to keep his side on level terms after 22 minutes. Grant Holt threaded the ball through to Wes Hoolahan who was left with only Guzan to beat but the United States international managed to block the shot with his left foot.
But then against the run of play Villa went ahead through Benteke's second goal since his £7million summer move from Genk after 27 minutes. Gabriel Agbonlahor held the ball up before releasing the overlapping Holman and his cross found Benteke completely unmarked.
The Belgian international had time to pick his spot before sliding the ball past Ruddy into the corner of the net.
Villa were reduced to 10 men after 52 minutes when Joe Bennett collected a second yellow card for a foul on Elliott Bennett.
Guzan made his second crucial save of the game when he blocked a rising close range attempt from Hoolahan after Anthony Pilkington had supplied the telling pass.
Guzan was again Villa's saviour when he saved Holt's low drive after he broke clear but he had no chance of preventing Turner's equaliser after 79 minutes. Pilkington's quickly taken corner picked out Hoolahan and his inswinging cross was met by Turner whose glancing header flew into the far corner of the net.