.The Sky Blues started brightly and went close in the first minute when Youssef Safri's clever reverse ball into the West Ham area nearly found Graham Barrett but David James came off his line well to claim.
The hosts then had a strong penalty appeal turned down in the fifth minute as they piled the pressure on the Hammers.
Andrew Whing played a good ball in from the right flank and Ian Pearce appeared to push Andy Morrell in the back but referee Graham Salisbury was unimpressed as the striker hit the deck.
Just nine minutes later West Ham took the lead against the run of play, but it was a trio of errors that led to the opening goal.
First Safri dawdled on the edge of the box, electing to pass to Gary McAllister instead of clearing - the City player-boss was then robbed easily by Jermain Defoe, who slotted the ball under Pegguy Arphexad, who should have done better.
However, with the first half winding down Coventry carved out a much-deserved equaliser.
Patrick Suffo turned well on the edge of the box and played in Michael Doyle whose cross found Barrett four yards out for a simple finish.
Rob Lee and Andy Morrell exchanged 30-yard efforts at each end - Lee's drifted wide but Morrell's tested James.
Christian Dailly then forced an excellent save from Arphexad when he rose to meet a Wayne Quinn cross.
Livewire Defoe then beat Doyle and Whing but Arphexad came off his line quickly to deny the England man the chance of the winner.