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 have a six-point lead for the first wild card into the playoffs from the Eastern Conference -- the Ottawa Senators hold the second wild card, tied in points with the Red Wings, Philadelphia Flyers and Columbus Blue Jackets -- and are six points out of third in the Atlantic.
"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."