Green should have hit the target but dragged a shot wide, and the striker was unlucky to be denied by a good block from Ben Turner just before half-time.
Green was in action again early in the second half, heading straight at keeper Keiren Westwood and then forcing him to parry a fierce left-footed shot following a swift counter-attack.
Chris Hargreaves was next to try his luck but could only shoot over the bar following DSane's cross, and Nicky Wroe was also off target with an opportunistic effort.
The missed chances eventually proved costly when Coventry took an unlikely lead.
Fox delivered the ball from the left into a crowded penalty area where Ward rose to head high into the neT.
That stunned Torquay, who were unable to mount a comeback in the dying minutes.
Torquay boss Paul Buckle: "We needed to go out and perform and we did that. We just couldn't find the net.
"We did everything but score - we really did - and if you are going to go out in the fourth round that's the manner to go out in.
"It was, by any standards, a cracking cup tie and we are proud to have been part of it."
Coventry manager Chris Coleman: "Twenty minutes from time I would have been happy with a replay.
"In the second half we were outplayed and outfought in many departments and Torquay deserved a lot more than they got out of the game.
"We had a lot of travelling fans here and they might have thought we were going to breeze it. We were never going to do that."
E-mail this to a friend 
Printable version 
Bookmark with:
What are these?