Steven Stamkos added a goal and three assists for Tampa (2-1-1), while Ondrej Palat also scored.
Anthony Cirelli chipped in with three assists and Andrei Vasilevskiy made 25 saves to get the victory as the Lightning emphatically halted an early two-game slide.
Auston Matthews, with a goal and an assist, John Tavares and Andreas Johnsson replied for Toronto (2-2-1).
Frederik Andersen allowed seven goals on 28 shots before getting the hook in favour of Michael Hutchinson seven minutes into the third period. Hutchinson finished with five saves.
Tampa’s top line of Point, Stamkos and Kucherov — which combined for 318 points in 2018-19 — registered 11 on this night in their first action together of 2019-20.