Gareth Southgate made four changes to team that were stuffed 5-0 by West Brom last week and he looked to be on track for the win after goals from Sean St Ledger and Rhys Williams.
But the Sky Blues fought back, first through Clinton Morrison and then through Leon Best, who turned the ball home deep into injury time.
Boro nearly made a great start after Coventry's Stephen Wright misjudged a first minute long ball.
Marvin Emnes broke through and almost knocked his shot past Keiren Westwood, but the keeper managed to block with his legs.
The Sky Blues sprung to life after the near-miss and should have taken the lead in the sixth minute when Morrison crossed to the unmarked Michael McIndoe, but the winger headed wide from six yards.
Coventry were dogged in midfield and their hard work almost produced a 28th minute opening.
Tough tackling in the middle saw the ball finally played to Morrison, who fought off two challenges to shoot from range but his effort went wide.
But a nightmare five minutes for the Sky Blues put Southgate's mate in control.
A superb corner from Adam Johnson in the 40th minute found St Ledger and the on-loan defender rose above his marker to head past Westwood.
Then in injury time, Gary O'Neil's cross was not cleared and eventually fell to Australian Williams, who fired home.
Coventry switched to a 4-3-3 and brought on Aron Gunnarsson and Patrick van Aanholt at the second half to try and salvage something from the game.
They came close through McIndoe and Wright and finally made the breakthrough in the 75th minute when Best's knock down allowed Morrison to spin his marker and fire into the net.
The home side pushed on, desperate for the leveller, and just as time seemed to be running out, a bouncing cross made it to the unmarked Best at the back post and his outstretched boot turned home the ball to earn his side the point.