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.
"We'd love to have home-ice," Brewer said. "Clearly it's something that you never want to use, but you'd love to have. The other thing is, you just want to play well going into the playoffs."
Boone Jenner and David Savard had goals for Columbus. The playoff-bound Blue Jackets are tied with Philadelphia -- which has one game at hand -- for third place in the Metropolitan Division.
"We just have to regroup," Blue Jackets right wing Corey Troop said. "We just need to take care of business on our end."
The Blue Jackets are also tied with Detroit, which will be one of the two Eastern Conference wild-card teams.
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.
"It's my biggest dream come true," Gudlevskis said.
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.
"If something were to happen and Gudie had to go in, I did not want his first game to be a playoff game," Lightning coach Jon Cooper said.
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.
The Blue Jackets took three penalties in the opening 4:42 of the second.
"That's something that you can't do going forward," Columbus coach Todd Richards said. "I looked down the bench and I think I used four or five forwards, six forwards, for the first five, six minutes of the second period."
Palat left in the third after taking a hard check. ... 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).
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TAMPA, FL - APRIL 11: Goalie Kristers Gudlevskis #37 of the Tampa Bay Lightning skates during the pre game warm up...