Tampa Bay snapped a six-game losing streak, with Ben Bishop stopping 26-of-28 shots in the victory.
St. Louis gave Tampa Bay a 2-1 lead late in the second period with his first goal of the game, but Joffrey Lupul tied the score by putting a slap shot past Bishop with 24 seconds to go in the middle stanza.
Radko Gudas put the Lightning in front for good 3:13 into the third and St. Louis added two more scores, the last of them coming into an empty net with 2:49 remaining.
St. Louis boosted his point total for the season to 58 and moved two in front of Pittsburgh's Sidney Crosby for first place in that category. Steven Stamkos scored his 29th goal of the campaign for the Lightning, moving him within two of Washington's Alex Ovechkin for the league lead.
Despite the offense provided by Stamkos and St. Louis this season, the Lightning will miss the playoffs.
Toronto has clinched its first post-season berth in nine years and will open on the road in the first round of the playoffs.
James Reimer took the loss, giving up four goals on 25 shots.
Celebrity Families of 2014 [PHOTOS]