The 30-year-old netted the only goal of the game and his sixth in as many games from the penalty spot just past the hour-mark after Danny Livesey had clumsily fouled on-loan Gills midfielder Danny Hollands.
Carlisle's day got worse as Lee Miller was sent off for an off-the-ball incident with Adam Barrett, but Gills defender Leon Legge was to receive a second yellow soon after for a foul on David Amoo.
It took Carlisle 30 minutes and Gillingham until the start of the second half to register a shot on target, although there was controversy at the end of the first 45 minutes.
The Cumbrians were adamant that they should have been awarded a penalty after Michael Harriman appeared to have blocked Matty Robson's goal-bound effort with his arms, but their appeals were waved away.
Kedwell's successful penalty came in the 63rd minute, while Carlisle striker Amoo wasted his side's best chance to equalise when he shot straight at home keeper Stuart Nelson before Miller and Legge saw red.