Miller made 40 saves, including Marco Sturm's penalty shot in the first period and Mark Recchi's shot from the edge of the crease as the final horn sounded, in a matchup of last month's USA Olympic goaltenders.
Tim Kennedy also scored for Buffalo, which moved one point behind Pittsburgh for second overall in the Eastern Conference.
The Sabres improved to 27-0-0 when leading after two periods, but had to hold on after Dennis Seidenberg scored to make it 3-2 with 5:37 to play.
"It was really big for us, especially with the spot they're in and the desperation they have," Myers said. "It was a huge road win for us. As a team right now, we're focused on moving forward."
David Krejci had Boston's other goal. The Bruins, who remained in eighth place in the East after Carolina defeated Atlanta 4-1, lost for the third time in seven games.
For the goal-starved Bruins, tied for last in the league in scoring, getting behind 3-1 early was just too much to overcome.
"We had an opportunity to get back in the game, but the goaltender made some good saves at some opportune times," Boston coach Claude Julien said.
Boston goalie Tim Thomas, Miller's backup in Vancouver, was pulled following the Sabres' third goal and left the ice to jeers. He was making his second straight start after shutting out Calgary on Saturday.
"The fact that I was leaving the ice? I don't know what they were booing," said Thomas, who agreed it was his most frustrating time since coming into the NHL late in 2003 season.
"You don't like to see it," Miller said of the boos toward Thomas. "We are competitive to a certain degree, but I know he's a little bit frustrated. I didn't think there was a whole lot he could do on at least two of those goals."
The Bruins grabbed a 1-0 lead when Krejci made a nifty move by faking to go behind the net from the right side before tucking a shot inside the post, beating Miller at 7:43 of the first.
Myers' goal tied it 2:13 later. He stole a clearing pass at the right point and fired a high shot that hit defenseman Dennis Wideman's arm and caromed by Thomas.
The Sabres made it 2-1 when Gaustad scored on a backhand from in close off a rebound midway into the opening period.
The Bruins, who had a big edge early in the first period with strong play and some good scoring chances, ended up outshooting Buffalo just 14-11 in the period.
Miller blocked Sturm's penalty shot when the winger shot it into his body at 3:20 of the first.
Kennedy completed a 2-on-1 break when he slipped a shot under Thomas' left pad 6:08 into the second period.
"You have to try and change the momentum," Julien said. "I don't think I have to try and justify anything. Like I said hindsight is 20-20. You look at Timmy's last game. He was extremely good. We expected that tonight."
When Thomas was lifted in favor of Tuukka Rask, he headed down the runway toward the dressing room and missed about six minutes of play.
Seidenberg's shot from the left wing hit Miller, popped over his left shoulder and rolled into the net.
It was the sixth time this season Thomas has been pulled from a game. Rask has never been removed. ... Buffalo's Derek Roy was held without a goal after getting a hat trick in a win over Tampa Bay on Saturday. ... The Bruins dropped to 3-10-3 at home since New Year's Day. ... Julien said he didn't have an update on injured defenseman Andrew Ference, but also said he would not be with the team in New Jersey on Tuesday.