"If you're going to get a break, you want to finish on a winning note," St. Louis said. "Keep the streak alive, and come back where you left off."
Columbus got goals from Brett Lebda and Ryan Johansen. The Blue Jackets, coming off a 4-1 loss at Nashville on Monday night, have lost four straight.
"We battled until the end," Columbus coach Todd Richards said. "You're looking for the energy, and I know there's circumstances that make it difficult at times, but I still thought for a 60-minute game that we could have and should have been better in certain areas."
Lecavalier put the Lightning ahead 2-1 on the power play with a re-directed goal from the low slot 8:19 into the second. The Tampa Bay captain has three goals and 10 points during a six-game point streak.
St. Louis made it 3-1 on an in-close goal off a pass from Lecavalier with 3:04 left in the second. St. Louis, who assisted on Lecavalier's goal, also extended his point streak to six games (eight assists, 10 points).
After Johansen cut the Columbus deficit to 3-2 from the low left circle at 5:40 of the third, Thompson got the goal back at 11:29.
Tampa Bay outshot the Blue Jackets 24-11 through two periods and 31-24 overall. Columbus, with an NHL-low 32 points, is 1-18-1 when behind entering the third period.
"Without question, there's guys that have proven over the season that they show up every night," Richards said. "We need a group of 20 doing it. If we're missing two, three guys, it's tough for us to win games. So that was kind of my message to the guys as they go rest and relax, when they come back, we need everybody every single night."
Angelidis stole the puck from Colton Gillies, skated into the Columbus zone and scored his first NHL goal -- coming in his first game -- by beating goalie Curtis Sanford on a backhander with 6:40 to go in the first.
"It's a dream come true," Angelidis said. "I was in shock. Did that really happen? I was trying to get it on net, just like a rebound kind of shot, and it found a way in."
Angelidis is the fifth Tampa Bay player, and first since Ryan Craig on Dec. 17, 2005, to score a goal in his NHL debut.
Lebda, signed as a free agent by Columbus last Thursday, tied it at 1 just 1:47 after Angelidis' goal on a shot from the low right circle that got past goaltender Mathieu Garon. It was the defenseman's first goal since last Feb. 24, and 20th overall in 369 NHL games.
"We made it a close game, but unfortunately they got that fourth goal," Umberger said. "We kept fighting and that shows some heart and character."
Lightning center Steven Stamkos, the NHL goals leader with 32, was held off the scoresheet. He got both of his two shots in the third and finished minus-1.
Tampa Bay D Victor Hedman missed his 13th straight game because of a concussion, but has resumed practicing with the team. ... Columbus D Nikita Nikitin sat out his second consecutive game due to a knee injury and will be re-evaluated after the All-Star break. ... Lightning C Dana Tyrell will undergo right knee surgery next week and is expected to be sidelined six months. ... Blue Jackets LW Vaclav Prospal has gone eight straight games without a point.
Copyright by STATS LLC and The Associated Press
Arena: Amalie Arena Location: Tampa, Florida
Referees: Marc Joannette, Marc Joannette Linesmen: Pierre Racicot, Michel Cormier