Casey Mittelstadt scored, and Jeremy Swayman made 20 saves for the Bruins (43-26-8), who have lost two straight after a four-game winning streak. They lead the Ottawa Senators by six points for the first wild card into the playoffs from the Eastern Conference and trail the Montreal Canadiens by four points for third place in the Atlantic Division.
"I didn't like the first few minutes. We gave up two odd-man rushes. ... We played a pretty good game, we really did," Boston coach Marco Sturm said. "A couple of bad bounces. We didn't get the puck in on the second one and all of sudden a good team like that, they take advantage."
Raddysh gave Tampa Bay a 2-1 lead at 14:29 with a wrist shot from a sharp angle in the right face-off circle that got under Swayman's right shoulder.
"It was just a shot on net," Raddysh said. "I knew (Kucherov) was in the middle and I was just trying to throw it on net. Fortunate for that one to go in."
Kucherov added an empty-net goal at 18:27 for the 3-1 final.
"I thought we had a lot of positives for our group. Sometimes you don't get the results," Swayman said. "Our team shouldn't be hanging their heads. A lot of great things came out of tonight's game and that's what we should be focused on."