With Rotherham and Northampton both losing, Kedwell's 15th goal of the season, a fine volley in the 48th minute, handed Gillingham the points and rubber-stamped their return to England's third flight.
The hosts were the better team throughout; Kedwell and Steven Gregory both tested Gulls stopper Martin Rice early on and Adam Birchall hit the bar with a curling effort after just two minutes.
After Kedwell had broken the deadlock, latching on to Joe Martin's diagonal pass, Chris Whelpdale had two curling efforts well saved by Rice, and Charlie Allen fired wide from close range as the home side sought a second goal.
Torquay's best chances came through former Gills loanee Rene Howe, who hit the post and had an effort cleared off the line within the space of a minute midway through the first half.
In a nervy finale, Kevin Nicholson also rattled the crossbar for the Gulls with a 25-yard free-kick five minutes before the whistle sent the home fans into rapture.