Carl Baker put Coventry in front with a well-struck free-kick from 20 yards out after 35 minutes, but the lead did not last until the break as the visitors were the beneficiaries of a harsh penalty decision seven minutes later.
Leon Clarke scored from the spot after falling in a clumsy coming together with Richard Wood.
The Iron could have gone into half-time in front, but the referee ruled that City goalkeeper Joe Murphy had been fouled before Clarke tapped in.
The striker should have made it two in the opening stages of the second half as he directed his free header straight at Murphy, but made no mistake with his next chance - sliding the ball under the on-rushing goalkeeper after a hopeful ball forward fell in his path in the 75th minute.
Coventry pushed for an equaliser late on, but Iron goalkeeper Steve Mildenhall produced two incredible reaction saves to deny Baker and Roy O'Donovan in stoppage time.