Vardy, whose goals fired Fleetwood into the Football League last season, began to pay back his £1million transfer fee with his first goal for Leicester.
Vardy wrapped up a comfortable victory in the 77th minute, heading home a majestic diagonal cross by the impressive Ben Marshall as Leicester cruised into the second round of the Capital One Cup.
But City were home and dry long before then.
Torquay held them for 20 minutes, before Lloyd Dyer punished a moment's hesitancy by home defender Joe Oastler to open the scoring in the 21st minute.
Marshall curled a 25-yard free-kick over the Torquay wall and into the top left-hand corner in the 33rd minute to extend the lead for the visitors.
Midfielder Matty James finished off a perfectly timed through-ball by the on-song Jermaine Beckford four minutes into the second half as Leicester went further ahead.
Only an offside flag stopped Vardy scoring his second and City's fifth near the end but by then the game was long over as a contest.