Ondrej Palat also scored for the Lightning, who took a one-point lead over Montreal for second place in the Atlantic Division. A runner-up finish would give Tampa Bay home-ice advantage in its first-round playoff series with the Canadiens.
Gudlevskis had played in the ECHL and AHL, and for Lativa in the Sochi Olympics this season. Anders Lindback started in place of the injured Ben Bishop in the Lightning's 4-2 win Thursday night over Philadelphia.
Bishop, 37-14-7 this season, might not be ready for the start of the playoffs due to an upper-body injury. Bishop left early in the first period of Tuesday's game against Toronto with what appeared to be a left elbow injury.
After Jenner scored a power-play goal at 13:46 of the second, Brewer gave Tampa Bay a 2-1 lead when he beat backup goalie Curtis McElhinney 1:08 later.
The Lightning took a 3-1 advantage on Brewer's second of the game and fourth this season with 1:54 left in the second. All four of the defenseman's goals have been scored in the last 12 games.
Savard pulled Columbus within 3-2 with 3:23 to go in the third.
Palat put the Lightning up 1-0 with a power-play goal at 3:55 of the second. The rookie has four goals and eight points during a six-game point streak.
NOTES: Tampa Bay C Valtteri Filppula (lower-body injury) and RW Teddy Purcell (flu) were late scratches. D Victor Hedman left after three shifts in the first period because of a lower-body injury. ... Blue Jackets RW Nathan Horton had surgery Friday for an abdominal injury and is expected to be out for six weeks. ... Tampa Bay D Sami Salo (upper-body injury) missed his second consecutive game. ... Columbus reassigned D Tim Erixon to Springfield of the AHL. ... The Lightning recalled C Cedric Paquette from Syracuse of the AHL. He had an assist in his first NHL game. ... Columbus C Ryan Johansen had an assist, giving him a five-game point streak (four assists, six points).