Wednesday had looked to be heading for a crucial win after Luke Varney had broken the deadlock in the 67th minute with a great finish from an acute angle, beating the formidable Keiren Westwood at his near post after a quick solo burst.
It was a fair result on the overall balance of play after Wednesday enjoyed the better of the opening 45 minutes against a below-par Sky Blues side, who were a different proposition after the break.
Coventry were sporting a commemorative white shirt to mark England's participation at this summer's World Cup, while at the same time supporting the country's bid to host the 2018 tournament.
But it was the visitors who threatened first after just five minutes, Darren Potter forcing Westwood to tip his shot around a post.
In what was an eventful start to proceedings, Wood saw his header cleared off the line by James O'Connor while Freddie Sears also threatened.
Westwood then again had to be at his best to keep out Eddie Nolan's right-footed effort as the game went from end to end.
Eight shots on target inside the opening 15 minutes told its own story and although Leon Clarke did find the net with a 20-yard strike midway through the half, it was ruled out for a foul in the build-up.
Within a minute Carl Baker stung the hands of Wednesday keeper Grant but as the frantic nature of the opening 25 minutes slowed so did the goalscoring opportunities.
And as the half-time whistle sounded, struggling Wednesday will have been the happier of the two sides as boos from the natives rang around the Ricoh Arena.
Signalling his thoughts on the first half, City boss Chris Coleman made a triple change at the break and introduced Clinton Morrison, David Bell and Chris Hussey.
And, having switched from 4-5-1 to a 4-4-2 formation, the hosts immediately looked a more settled outfit and twice went close from set plays before Morrison saw his finish ruled out for offside.
Yet the visitors survived the early second-half pressure and, with the game very much in the balance, Republic of Ireland international Westwood tipped Clarke's header wide.
James McPake then came within inches of breaking the deadlock for Coventry before Varney finally snatched the breakthrough.
The midfielder swept past Bell with ease out wide and, taking advantage of some questionable Coventry defending, fired home at the near post from a tight angle.
But, as the encounter entered the final 10 minutes, who else but former Owls skipper Wood levelled matters following confusion in the visiting defence between Grant and Purse.
Grant did, however, later save well to deny Baker what would have been a sure-fire winner for Coventry.