J.T. Miller and Will Cuylle also scored for the Rangers (22-25-6), who ended a three-game losing streak and won for the second time in 10 games.
Quick made 21 saves in his first win since Nov. 7 and the 408th of his career, moving him past Glenn Hall and into 12th place on the NHL's all-time goalie wins list.
David Pastrnak had three assists, the third being his 900th career NHL point, and extended his point streak to seven games (two goals, 10 assists). The winger became the 135th player in NHL history and sixth in Bruins history with at least 900 points. He is the second-fastest Bruin to hit the mark behind Phil Esposito (552 GP).
Pastrnak also moved past Rick Middleton (898 points) into sixth place on the Bruins' all-time scoring list.
"Obviously bittersweet," Pastrnak said. "It's always tough to enjoy these kinds of milestones when you don't get the win. But it's special, obviously. From the first period, I knew I'd be a disher today. I saw the ice well today. Unfortunately, we didn't get the 'W.'"