Tyler Bozak scored shorthanded and Matt Frattin added a goal for the Leafs (6-5-0), who won their second straight of a three-game road trip. Kessel's goal ended a frustrating drought for the top-line winger who had 37 goals last season.
There was no scoring the first period but the Jets came out fast and hard with four shots on goal before the Leafs had one — no repeat of Tuesday's flat start against the Panthers.
Redmond, from the Jets' AHL farm team, scored his first NHL goal thanks to a 2-on-1 short-handed breakaway initiated by Bryan Little, who fed him a cross-ice pass the rookie fired past James Reimer's glove hand.
Dion Phaneuf was the only Leaf between the two Jets and Toronto's Manitoba-born goaltender.
Clitsome put the Jets ahead in the third with a bullet slapped from just inside the blue-line that beat Reimer's glove hand again. It was his second of the short season and a little reminiscent of the kind of shot injured defenceman Dustin Byfuglien can unleash.
Cody Franson fired a shot that Frattin got credit for as the puck glanced off him past a downed Pavelec to tie the game at 14:58.
Kessel popped in Bozak's drop pass less than a minute later after the Jets took a holding penalty.
Pavelec stopped 15 shots while Reimer made 23 saves.
The Jets went 0-for-4 on the power-play.
Notes: The Jets leading scorer this season, defenceman Tobias Enstrom, went into Thursday's game riding a new career point streak and extended it to eight with another assist against the Leafs.