The Sky Blues made it back-to-back home wins after another late winner at the Coventry Building Society Arena.
The Sky Blues fell behind before the break after John Swift converted from the spot, despite City controlling the first half.
City picked up where they left off in the second 45 minutes and continued to dominate and were rewarded when Jamie Allen struck an equaliser, minutes after coming off the bench.
Then, deep into stoppage time, Matty Godden marked his return to the side, scoring in the 98th minute to secure all three points.