The Sabres swept the home-and-home series to improve to 5-0 against Boston this season, with the last four one-goal games.
"They're tight games," said Briere, who has seven points in four games since returning from a sports hernia that sidelined him for 24 games. "I thought tonight we had the better chances."
The win came three days after Buffalo rallied from a 2-0 deficit in Boston for a 3-2 victory.
"Maybe we didn't deserve that win the other night, but we wanted to come back here and show them that we have the better team," Briere said. "We did that tonight."
The line of Briere, Hecht and J.P. Dumont combined for 11 points in the two games.
"We're playing really well together," Hecht said. "We have good chemistry out there and it shows."
"We wanted to have a better start tonight, and that's something we talked about," Pominville said. "I think we played solid defensively, and that gave us our chances offensively."
Buffalo goalie Ryan Miller made 25 saves for his second straight victory.
Miller helped preserve the win with two stops while the Bruins played with an extra attacker over the final minute.
Buffalo closed within four points of the Northeast Division-leading Ottawa Senators, who were idle.
The 10th-place Bruins failed to gain ground on eighth-place Montreal in the race for the final Eastern Conference playoff slot. The Canadiens remain seven points in front of Boston after losing to Toronto on Tuesday night.
Bergeron gave Boston a 1-0 lead at 8:59 of the first period when Brad Boyes' shot from the left circle went off his skate in front of Miller. It was Bergeron's 20th goal of the season.
The goal stood after a brief replay review.
Pominville tied it 2½ minutes later with his 15th, wristing a shot past Boston goalie Tim Thomas with Buffalo on the power-play.
Jurcina made it 2-1 with a power-play goal early in the second, but the game turned when Boston went without a shot in the final 12½ minutes of the period. During the drought, Buffalo took the lead for the first time by scoring twice.
"We got away from our game plan," Boston coach Mike Sullivan said. "It was a combination of us getting away from it and Buffalo being a good team that will make plays."
With the Sabres enjoying a four-on-three advantage, Vanek tied it at 2 with his 20th goal 11:37 into the second. He deflected Ales Kotalik's shot from the point.
Hecht made it 3-2 with his 17th of the season with 3:51 left, banging home a rebound after Thomas stopped Briere's original shot from close in.
Thomas finished with 32 saves in his first start in three games.
Nine of the Bruins' last 10 losses have been by one goal, including six straight.
"Once we have a lead we have to try and keep it," Boston forward Sergei Samsonov said. "It's two frustrating losses."
The Sabres have won 39 games this season, the most after 60 games in team history. ... The two teams will meet for the third time in nine days on Sunday in Buffalo. ... Boston forward P.J. Axelsson missed his third straight game because of a knee injury sustained March 1 against Carolina. ... Samsonov played despite injuring his knee in practice on Monday after colliding with winger Josh Langfeld. ... Langfeld played in his 100th NHL game. ... Vanek became the 11th Buffalo rookie to score 20 goals in a season. Vanek didn't score his first goal until the 15th game of the season.