Matthews one-timed a cross-crease pass from Mitchell Marner on the power play for his 47th goal of the season and a 2-1 lead.
The Maple Leafs, who lost all three games of a California road trip last week, scoring three goals, defeated the Lightning 4-3 on Feb. 25.
"It could be the divisional kind of rivalry (that led to the strong efforts), and obviously we know they're a really good team, so I think we'd like to find ourselves playing more consistently like we have in (those games against Tampa Bay) no matter who it is against and have starts like we did tonight, no matter who we are playing," Matthews said.
WATCH: [All Lightning vs. Maple Leafs highlights]
Ondrej Palat scored, and Andrei Vasilevskiy made 34 saves for the Lightning (43-21-6), who trail the Boston Bruins by eight points for first place in the Atlantic and lead the Maple Leafs by 11.
"It was disappointing tonight," Tampa Bay coach Jon Cooper said. "During the course of a year, 82 games, three periods a game, that's a lot of periods of hockey, and for the most part we have a lot of good ones, a small amount we could have been better and couple that are embarrassing, and that would fall under the embarrassing category.
"If you're not going to compete hard, be physical and do things you need to have success, you'll chase a team like that around the rink all night, and that's what we did, especially in the first period."
William Nylander scored, and Frederik Andersen made 32 saves for the Maple Leafs (36-25-9), who moved three points ahead of the Florida Panthers in the Atlantic. Toronto was 2-for-5 on the power play and 4-for-4 on the penalty kill.
"The special teams were clearly the difference in the game tonight, not unlike our last game in Tampa Bay," Toronto coach Sheldon Keefe said. "That was good for us, and we got a really good start to the game in the first period and were well in control."