Kuhlman, who hadn't played since Game 3 of the Eastern Conference Second Round against the Columbus Blue Jackets on April 30, scored after Blues defenseman Alex Pietrangelo turned the puck over near the blue line. His shot went over Binnington's right shoulder and under the crossbar to make it 3-0 at 10:15 of the third period.
Kuhlman replaced forward David Backes, who had gone six games without a point.
"One thing [Kuhlman] does, he brings some speed, he gets in on the forecheck with his foot speed," Bruins coach Bruce Cassidy said. "David is more of a physicality guy. [Kuhlman] can make some plays as well, and that shot, he's sneaky with his wrister. He's scored a couple times, that righty across the body.
"I don't want to give away state secrets here, but he does have that shot. Most righties want to go glove side. He's able to find the blocker side."
Kuhlman is the 21st different Bruins player to score at least one goal this postseason, which ties the NHL playoff record for most unique goal scorers by one team (1987 Philadelphia Flyers).
"It's been a little bit," said Kuhlman, who hadn't scored since April 2 against Columbus. "But at the same time, you come into every game just trying to work hard, and [I] was fortunate to see that one go in."