The Tigers began the match missing five of their main first team squad, but they did manage to start the match the brighter with Stuart Elliott's dangerous cross across the box being hastily put out in the first minute.
Elliott then shot wide after the seventh minute, and after 12 minutes Richard Hinds' shot deflected wide from 25 yards.
But Torquay began to take over, and Damien Delaney superbly blocked a ten yard shot from Kuffour by sticking a foot out in desperation after lax defending left the Tigers exposed.
Then, after 15 minutes, two excellent instinctive saves from Boaz Myhill - the first from a long range free kick, the second from another good effort from Kuffour in the box - ensured City were not behind.
After 24 minutes, David Graham was let in by another lax spell of defending, and Myhill pulled off an excellent save to deny him from 15 yards.
A minute later Kuffour shot wide from about 25 yards after a mix up in midfield, before Graham was allowed to shoot off target as the Tigers looked increasingly uncomfortable.
On the half hour mark Delaney did well to block a shot into the box from Graham after more clever work from Kuffour caught out the midfield again.
But minutes later Kuffour pulled up with a muscle injury and was replaced by Gritton, initially allowing the Tigers to stabilise and put a bit of pressure on Torquay.
After 43 minutes Jonathan Walters shot into the side netting in City's best chance, but the Gulls raced away immediately and Graham had another chance to shoot - but wasted it again, blasting well over.
But the inevitable happened in first half injury time when Alex Russell played on a Kevin Dearden clearance to Graham, who released it to Gritton, and with the back four nowhere the substitute showed good composure to round Myhill and shoot into an empty net.
Elliott had a great chance to level after the restart but stumbled in the box. After 54 minutes Graham shot just wide as Torquay resumed their dominance but a minute later Ben Burgess shot just over.
After 58 minutes a great cross from Burgess found Elliott at the far post, but Torquay blocked, before an excellent centre by Lee Marshall was perfectly placed on the head of Delaney but he headed tamely at Dearden.
Matt Hockley saw a shot thunder off the bar and Gritton missed a sitter deep into injury time and although City had Torquay fans hearts in their mouths in the last few minutes Torquay were well worth their victory and could easily have had more goals.