Christian Benteke (27) had set the hosts on their way to a first league win in five but Villa were finally made to pay for Joe Bennett's second-half dismissal and Turner's finish (79) was just reward for City's subsequent dominance.
Lambert had played down his continuing legal dispute with the Carrow Road club in the build-up but it was hard to believe that this, for him, was just another game: this missed opportunity will grate.
Tension there may have been in his dugout but it was sure in evidence on the pitch for both sides - just two wins between them so far - as the early play was pockmarked by loose balls and careless passes.
Benteke looped an early header towards John Ruddy's goal and Brett Holman found the target, but Norwich had the space and the intent to attack a defence deep and vulnerable-looking.
Ron Vlaar's nudge on Elliott Bennett in the box might well have had consequences (17) but the first key moment came soon after at the other end when Grant Holt poked into Wes Hoolahan's path, only for Brad Guzan to stop the goalbound clip with his left leg (22).
The opener came then against the run of play but Villa cannot be picky these days and when Benteke controlled Joe Bennett's cross and gently curled beyond a stranded Ruddy, the relief was audible.
Norwich had been given a jolt and might have got another soon after the restart had Ruddy not pushed a Benteke header to safety but Joe Bennett's sending-off (52) - a push on Elliott Bennett yielding a second yellow - gave them unexpected impetus.
Guzan pushed away one Hoolahan shot, then another, before Robert Snodgrass came on - superfluous defender Elliott Bennett the man to make way - to add further attacking weight and saw a fierce volley well blocked.
Villa finally deployed Darren Bent at the expense of their goalscorer but he remained on the periphery as his team-mates tried to combat chaos in their box, Vlaar's block denying Snodgrass what surely seemed the equaliser.
Instead parity came from the resulting corner, Hoolahan affording Turner a header that drifted tantalisingly towards the far post and crossed the line via the goalframe.
This was professional as well as personal for Lambert - a chance to still the dissenting voices after Villa's worst start to a season in more than 25 years - but he and his side exited to boos, just one win in 19 now to their names.
Norwich fans gleefully chanted 'there's only one Chris Hughton' but their new man too has work to do, their side just three points off the drop zone.