Phil Kessel, Shawn Thornton and Chuck Kobasew also scored for Boston, which increased its lead in the Eastern Conference quarterfinal to 3-0 despite the absence of left wing Milan Lucic, who sat out a one-game league suspension.
Ryder, a healthy scratch for all but four of Montreal's 12 playoffs games last season, put Boston ahead 17:21 into the second period.
"I'd forgotten about last year. I don't really think about it," said Ryder, who signed a three-year, $12 million free-agent contract with Boston. "It feels like I've been here for so long now, actually, and the guys are great and they've welcomed me in and it's good just to be a part of the team. We're rolling good right now."
"I'm sure everybody would like to hear the word 'justice,' but that's not for me to say," said Bruins coach Claude Julien, who was himself relieved of his duties behind the Canadiens' bench midway through the 2005-06 season by Montreal GM -- and current head coach -- Bob Gainey.
"I think we're just kind of happy we were able to sign him," Julien said of Ryder, "and he's played a big role for us this year."
Kobasew scored into an empty net with 37 seconds remaining.
"At this point, there's not too much positive there," Canadiens Saku Koivu said. "Every game, there are things you try to build on but what we're doing right now is not enough. We have to find a way to get the goals. It doesn't matter how you do it, to get the win."
Price, pulled Saturday after allowing five goals through the first two periods, made 26 saves in his third consecutive start.
The Bruins, who haven't won a playoff series since 1999, are poised to beat the Canadiens for only the eighth time in 32 playoff matchups between the longtime rivals.
Game 4 is Wednesday night at the Bell Centre.
Lucic was suspended Monday by league disciplinarian Colin Campbell after he was assessed a match penalty for cross-checking Montreal's Maxim Lapierre late in Saturday's 5-1 win in Boston.
Left wing Alex Tanguay and defenseman Mathieu Schneider were both injured and unable to play for Montreal. The Canadiens, already without injured top defenseman Andrei Markov, announced moments after the opening faceoff that both key players were sidelined by upper-body injuries.
"I didn't even know they weren't playing until pretty close to warmups," Higgins said. "To miss those guys, that's a lot of skill that you've got to replace."
Weber, who made his playoff debut Saturday, remained in the lineup and collected two points, including an assist as Higgins gave the Canadiens their first lead of the series when he opened the scoring with his second goal 11:52 in.
Buoyed by a sold-out Bell Centre crowd of 21,273, Montreal pressed hard in the opening period, creating a number of scoring chances that drew the fans out of their seats.
"We liked the way we came out," Canadiens right wing Tom Kostopoulos said. "The crowd was a huge part of the first period."
Montreal's 1-0 advantage lasted all of 6:43, though, erased when Kessel scored his third goal at 18:35, allowing the Bruins to head off to their dressing room with a 1-1 draw through the first 20 minutes.
Thornton, who scored six goals in 79 games during the regular season, gave Boston a 2-1 lead when he scored 3:36 into the second.
Thornton recorded his first point in 25 playoff games overall when he beat Price from the left side of the slot with a shot inside the left post after taking a setup pass from behind the net by Byron Bitz, who took Lucic's spot in the lineup and made his playoff debut.
"Any time I score, I'm excited because I'm not getting 50 a year, that's for sure," Thornton said. "My linemates did an unbelievable job. I threw it on net and it was lucky enough to go in for me, but Bitzy did a great job hanging onto that puck and making a good play. Any time we can chip in, it's a plus."
Weber tied it at 2 with his first playoff goal at 5:16.
- Thornton won a Stanley Cup with Anaheim in 2007, playing 15 games without recording a point for the Ducks. He has appeared in 10 playoff games with the Bruins.
- Canadiens D Ryan O'Byrne dressed for the first time in the series, and LW Gregory Stewart made his playoff debut.
- Weber had one assist in three regular-season games.