BOSTON — This time, the Boston Bruins didn’t get off to a slow start.

It made a difference.

“It’s something we’ve talked about,” Tuukka Rask said after making 26 saves in a 3-1 victory over the Buffalo Sabres on Saturday that completed sweeps of both a home-and-home set and the four-game season series with the Sabres.

“We want to get that first goal more often,” Rask said. “I thought we came out really strong today — like we wanted to. It paid off today. It’s something we have to do more often.”

After falling behind 3-0 and 2-0 the last two games and by either 2-0 or 3-0 in six of the last 12, Boston came out strong, built a 3-0 lead and then finished off the first series sweep by either team in the history of the rivalry between the old Adams Division foes.

Boston outscored Buffalo, 13-4, in the four games.

Frank Vatrano, Patrice Bergeron and former Sabre Tim Schaller scored goals to build the lead as the Bruins (20-15-4) won for only the second time in their last six home games — squaring their home record at 9-9.

“Being from Mass. growing up, everyone’s dream was to score here in the Garden,” said Vatrano, who has two goals and four points in five games since coming back from foot surgery.

Former Boston University star Jack Eichel cut into the Bruins lead with 21.2 seconds left in the second period on his seventh goal in 15 games this season.

After the game, Eichel was anything but happy with the goal or anything else, slamming equipment, screaming and then leaving the room without talking to the media.

“I think every one of us should be. … We should all find that desperation, that urgency, that anger,” said coach Dan Bylsma, whose team is 1-4-2 in its last seven and is in last place in the Eastern Conference.

Added Sam Reinhart: “It’s frustrating now. Something has to change and it has to come from the inside.”

The game was a chippy affair, with the teams still upset at each other for Thursday’s events.

William Carrier, who knocked Boston’s David Backes out indefinitely with a concussion (the Bruins made the official announcement during the game), didn’t play because of a hand injury but there was still plenty of hard hitting.

The Sabres (13-15-8) lost two players in the first period — Johan Larsson suffering what appears to be a dislocated wrist on a heavy hit by Adam McQuaid, and Josh Georges leaving because of a hip pointer. Gorges was seen limping as he left the locker room.

Much of the hitting was done by the Bruins early, as they came out determined to shed their early-game problems — and they did it against the Sabres.

Rask improved to 19-7-3 this season and 13-5-1 lifetime against the Sabres (4-0 this season). He and the Bruins killed a 67-second two-man disadvantage in the first period.

The Bruins’ power play, hardly a strength all season, came through for the fourth time in the last five games when Bergeron scored.

Robin Lehner had 25 saves but fell to 8-12-5 — only 3-10-3 lifetime against Boston. He has started more games against the Bruins (17) than any other team.

The Bruins are 11-1-2 in their last 14 games against Buffalo, 6-1-2 in their last nine at home.

“We played much better — better start,” said Bruins coach Claude Julien, whose team has won one more game than it has lost. “We were playing with the lead, which makes a big difference. In the third period we played smart.”

Meanwhile, Backes is in the NHL’s concussion protocol after suffering the injury in the first period of the Bruins’ 4-2 win at Buffalo on Thursday.

Backes was hurt when he took a hard hit from the Sabres’ William Carrier. Backes flew backward before hitting the ice and remained down for a brief period. He needed help to get off the ice.

Carrier was sent to the penalty box for an illegal check to the head.

Backes has been sidelined with a concussion in the past. Backes, 32, has played in 33 games this season and has nine goals and 10 assists. He leads the team in hits with 98.

NOTES: Bruins LW Brad Marchand, who had an assist, talked pregame about taking on a Buffalo Twitter basher who threw a homophobic slur at him concerning he and Zdeno Chara. Marchand’s counter-attack resulted in account deletion. “Nowadays it’s not right to go after people that way so I figured I’d get it out there,” he said, adding he “has a few friends that are in same-sex relationships” and that “He (the basher) ended up deleting his Twitter.” … Buffalo D Rasmus Ristolainen came in with assists on 29.2 of his teammates’ goals, No. 3 in the league, and assisted on Buffalo’s only goal, his 16th point in the last 14 games and his 22nd assist of the season. … Denna Laing, who suffered a severe spinal injury in a game last Dec. 31 that was part of last year’s Winter Classic, dropped the first puck. … The Bruins hung team jersey Nos. 10 and 19 on their bench in warmups to honor James Lavin and Owen Higgins, the Plymouth high school players killed recently in a car accident. Their names were on the backs of the shirts. … The Bruins are at New Jersey on Monday, the Sabres at the Rangers on Tuesday.