Damien Delaney had to dive across to block a 15th minute Jo Kuffour shot. Goalkeeper Boaz Myhill then had his work cut out to make a number of saves, while more poor finishing from Torquay saw the ball end up in the South Stand from more chances.
City were sloppy with the ball, and were punished just inside stoppage time. Alex Russell flicked on and Martin Gritton - who had replaced the injured Kuffour - rounded Myhill on the edge of the box and fired into the empty goal under chase from Delaney.
Tigers manager Peter Taylor reshuffled his pack and changed to a 4-3-3 formation as City looked to get back into the game in the second half. Ben Burgess shot over on 54 minutes, then provided dangerous crosses for Elliott and Delaney, neither of whom could find the net.
Andy Holt had to make a good tackle in the box, before Taylor changed his side around again with a double substitution, bringing on Ryan France and Nathan Peat with 25 minutes to go.
Burgess was wasteful in the 70th minute and was substituted a minute later for Jamie Forrester - a decision that was popular with a large number of the 15,222 fans at the KC Stadium.
An effort from a Torquay corner was headed off the line by Peat, before Elliott was guilty of wasting what was probably City's best chance of the match. Stuart Green played it down the right channel, and after Elliott took it off Jon Walters' toes, he went past goalkeeper Kevin Dearden. However, his right-foot shot couldn't beat Tony Bedeau on the line, and Walters will have felt he could've done better.
Elliott had another opportunity with 10 minutes to go but headed France's right-wing cross wide.
Neat play between Forrester and Green almost let the midfielder in on goal but he was unlucky.
Torquay could have made the three points safe as Matt Hockley hit the post, then David Graham shot wide soon after. Elliott had the last chance at the other end deep inside stoppage time but headed Forrester's cross wide - a fitting end for a poor display, and the visitors will be satisfied they deserved to knock Taylor's men off the top of the table as they move into the top 7 themselves.
City line-up (4-4-2): Myhill; Thelwell, Joseph, Delaney, Holt (Peat 66); Marshall, Hinds (France 66), Green, Elliott; Walters, Burgess (Forrester 71).
Un-used subs: Musselwhite, Melton.