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 result means Martin Allen's side are 14 points clear of third-placed Northampton, who have four matches remaining, and 18 ahead of sixth-placed Rotherham, who have five matches left.
Cheltenham also lost, 2-0 at struggling Plymouth, meaning they are 14 points off the Gills with three matches left. Fifth placed Burton Albion were also beaten, hammered 7-1 by second-placed Port Vale, who are all-but promoted, nine points clear of the chasing pack with the best goal difference in the division.
Rotherham's chances of automatic promotion took a blow with a 2-1 loss at Morecambe. They have a mathematical chance of going straight up but are 13 points shy of Vale.
Northampton will probably also have to be content with the play-offs after they lost 1-0 at Bradford, who are just two points short of the top six. Exeter in seventh also lost, 1-0 at home to Dagenham.
Fleetwood's play-off chase took a blow with a 3-0 home defeat to Rochdale, as did Oxford's after a 1-0 home loss to Wycombe. Mid-table Chesterfield and Bristol Rovers won 2-0 and 1-0 respectively at struggling Barnet and fellow relegation-battlers AFC Wimbledon.
The battle to stay up took another twist thanks to Plymouth's win, which hauls them out of the drop zone, while Accrington drew with fellow strugglers York City. Bottom club Aldershot did not play.
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