Boston scored first but Toronto had the last laugh, beating the Bruins 4-1 for a 1-0 games lead in the best-of-seven first-round series.
It’s the Leafs first Game 1 victory since April 9, 2003 against the Flyers.
Mitch Marner led the way with two goals, including on a short-handed penalty shot.
William Nylander and John Tavares, into an empty net, had the others.
Frederik Andersen turned aside 37 shots.
Game 2 goes tomorrow night in Boston before the series shifts here Monday and Wednesday.
Meanwhile, the Raptors open the playoffs against Orlando at Scotiabank Arena tomorrow at 5 p.m.
Mayor John Tory and members of city council will host representatives from Maple Leaf Sports & Entertainment at a flag raising today at 2 p.m. on the podium roof of city hall to celebrate and support their playoff runs.
In recognition of their first home games, the mayor will proclaim Saturday Raptors Day and Monday Blue & White Day.
Team flags will fly all day on the podium roof before being transferred to the Queen Street flagpole for the duration of their playoff runs.