But after Yorke had headed the Black Cats into an early lead, Coventry had the better of the chances to draw level only to be dealt a cruel sucker-punch by Edwards' superb late strike.
Coventry should have been off to a flying start, Leon McKenzie being guilty of a dreadful miss in the second minute after complete disarray in the home defence.
Kevin Thornton jinked his way through but McKenzie, completely in the clear, had his close-range shot turned behind by Darren Ward.
Sloppy defending in the Coventry defence let in Edwards who found Daryl Murphy but a weak shot was easily saved by Luke Steele and then a promising run and cross from Edwards was just beyond Stern John.
A poor challenge by Andrew Whing in the 18th minute on Dean Whitehead earned the full-back a booking and, from Ross Wallace's resultant inswinging free-kick, Sunderland went ahead.
Confusion reigned in the penalty area when Stan Varga challenged and Yorke reacted first to the loose ball in the air and headed firmly just inside the post.
The lively Michael Mifsud carved open the Black Cats defence, gliding his way past three defenders only to be denied by Danny Collins, and then the Maltese star forced Ward into another great save on the half-hour as Coventry continued to give as good as they took.
But they suffered a big blow in the 34th minute when Kevin Thornton, at the heart of nearly all their attacking moves, went down heavily in a midfield challenge and, after lengthy on-field treatment, was eventually stretchered back to the dressing-room and replaced by Jay Tabb.
Sunderland twice went close to increasing their lead just before the interval, Varga heading weakly at Steele from Whitehead's cross and John shooting just past the post when set up by Edwards.
Coventry, who brought on Adam Virgo for Marcus Hall at the start of the second half, pressed strongly with a shot-cum-cross from Mifsud bouncing off the top of the bar and a 25-yard free-kick from Whing whistling just past the post with Ward at full stretch.
Roy Keane sent on Anthony Stokes and Tobias Hysen just after the hour but Coventry continued to force the pace with Ward making another stunning save from Kevin Kyle who played on despite suffering a painful hand injury.
The Black Cats, however, made the three points save in the 84th minute, a stunning volley from Edwards taking a huge deflection to wrong foot Steele.
Stokes had a shot saved and John headed just past the post as further gaps appeared in the Coventry defence in the vain hope of salvaging a point.