Brad Marchand and David Krejci, with a goal and an assist each, and David Backes and Sean Kuraly rounded out the scoring for Boston, which got 26 saves from Tuukka Rask. Torey Krug added two assists.
Zach Hyman replied for Toronto, while Frederik Andersen made 35 stops.
Game 2 of the Eastern Conference quarterfinal goes Saturday night at TD Garden before the series switches to Air Canada Centre on Monday.
The Leafs talked at length ahead of Thursday’s game about how containing the line of Marchand, Pastrnak and Patrice Bergeron – a trio that combined for 99 goals in the regular season and is stellar in all three zones – would be crucial.
They have plenty of work to do in that department after a six-point performance in Game 1 that also saw Marchand, Bergeron and their teammates take the body to the young Leafs at almost every opportunity.
Toronto’s Nazem Kadri took exception to an elbow to Mitch Marner from Tommy Wingels in the third period and replied by taking a run at the Bruins forward. He earned a five-minute major for charging and a game misconduct.
Boston limited space in the neutral zone at even strength as Auston Matthews, Marner and William Nylander struggled to find room to operate.
Toronto’s power play, which had been operating at 32.2 per cent since the end of January, will also be a point of emphasis after going 0 for 3, while the penalty kill allowed Boston to score three times with the man advantage.
Backes snapped a 1-1 tie on the power play at 15:43 of the second when he chipped a loose puck up and over Andersen at the lip of the crease after Leafs defenceman Ron Hainsey could only get a piece of a pass in front.
The Bruins’ second goal with the man advantage came after the Leafs wasted two power-play chances of their own earlier in the period.
Boston stretched its lead to two with 38 seconds left in the period when Pastrnak took a feed from Marchand out of the corner and zipped a shot past Andersen’s glove.
Marchand was at his agitating best earlier in the period when he nudged Leafs defenceman Nikita Zaitsev into Andersen to draw a crowd after getting caught on television replays appearing to lick the face of Leafs forward Leo Komarov in the first.
Toronto killed off two penalties to start the third, but Kuraly made it 4-1 when he batted the puck out of mid-air after Andersen robbed Pastrnak.
Wingels elbowed Marner in the corner midway through the third, leading to Kadri’s five-minute major and game misconduct.
Krejci made it 5-1 from a horrible angle on the power play at 11:29.
Both bounced in the opening round of last season’s playoffs, Boston and Toronto came into the series with big expectations, and with the knowledge one team will be left bitterly disappointed at its conclusion.
The Bruins finished the regular season with 112 points, good for second in the Atlantic Division and fourth in the overall standings. The Leafs, meanwhile, wracked up a franchise-record 105 points, which earned them the division’s third seed and the league’s seventh-best record.
Boston stormed out of the gate in the first inside a raucous TD Garden, and grabbed the lead on the power play at 5:28 when Krug fed a pass between the skates of Leafs defenceman Roman Polak off the rush to Marchand, who beat Andersen on a move to the backhand.
Andersen made a couple of big stops to keep the deficit at one before Hyman tied it on a great individual effort at 16:52. The winger fought off both Krejci and Charlie McAvoy down the right side before tucking a shot beyond a sprawling Rask moments after Toronto blue liner Jake Gardiner hit the post.
The Bruins and Leafs last met in the playoffs back in 2013, a series that saw Toronto become the first team in NHL history to blow a three-goal lead in the third period of a Game 7 before Boston eventually won it in overtime.
There’s been plenty of turnover on both sides since, but the Bruins’ core that made it all the way to Stanley Cup final that year remains largely intact.
Matthews had four goals to lead Toronto during its six-game defeat to Washington last spring, a series that gave the superstar centre and his young teammates a first taste of playoff hockey at this level.
They got another lesson Thursday about what it takes to win at this time of year.