Turgott came off the bench to score the winner and hand City their third away win on the spin.
Tony Mowbray's men had the first chance, when Dominic Samuel had a chance after just five minutes when he latched onto a defensive lapse on the half-way line and drove towards the area, curling a finessed effort inches wide of the right post from 20-yards.
With five minutes to go to the break, Marcus Tudgay broke down with what looked like a re-occurrence of his hamstring injury, with Sanmi Odelusi taking his place.
That was the last action of a dull first-half but the hosts came out stronger in the second-half, with former Sky Blues loanee Luke Williams coming on at the interval for the Posh.
Jack Payne then went close for United after he hit the side netting from 20-yards with the crowd thinking the ball had gone into the net past Lee Burge.
Turgott then came on for Frank Nouble and provided the opener just 11 minutes after coming on, when Odelusi picked the ball up outside the box and had a pop shot which deflected up into the air and Turgott scooped a clever finish into the far corner inside the area for his first goal for the club.
Moments after the goal, Burge had to be at his best as he made a spectacular save to deny Payne's 25-yard lopping effort which was flying in.
City grew into the game after the opener and they had a good penalty appeal turned down when Odelusi looked set to tap in Samuel's cross but he tangled with Michael Boswick and the referee waved away vehement City protests.
City had to defend extremely well to take the three points and almost had a second, when Turgott hung the ball in and Samuel met it at the back post but tapped the ball against the upright.
After that chance City had to hang on in four minutes of added time but defended extremely well to claim their third win under new manager Mowbray.
Coventry City: Burge (GK), Willis, Pennington, Martin, Stokes, Ward, Fleck, O'Brien (C) (Webster 90), Tudgay (Odelusi 40), Nouble (Turgott 58), Samuel.
Subs: Charles-Cook (GK), Phillips, Barton, Thomas.
Peterborough United: Alnwick (GK), Smith, Burgess, Brisley, Ntlhe, Taylor, Bostwick, Payne (C), Newell (Maddison 67), James, Washington (Williams 45).
Subs: Henry (GK), Sheehan, Pearson, Beautyman, H. Anderson.
Attendance: 7,225 (857 SBA)
Referee: I Williamson