Kyle Connor scored for the Jets (21-25-7), who have lost three of four (1-2-1). Connor Hellebuyck made 33 saves.
"I thought early on we were able to advance the puck and create some chances," Winnipeg captain Adam Lowry said. "In the second period I think we started feeding into that transition game. They do a great job of stretching guys out. ... We kind of fed into that. It's just management. It's frustrating because I thought we had been playing a decent hockey game."
Dominic James gave Tampa Bay a 1-0 lead at 14:58 of the first period with a shot from the left circle after Raddysh sent him in following a stretch pass by J.J. Moser.
Raddysh extended the lead to 2-0 at 1:37 of the second period with a low slap shot from just inside the blue line, scoring for the third straight game.
"I think we got away from what we wanted to in the second period a little bit,” Raddysh said, “but we did what we wanted in the third and played in their end and shut them down a little bit to keep momentum on our side. Guys are buying in. They know what the job is and everyone is pulling their weight."
Connor made it 2-1 at 12:25, scoring in the left face-off circle on a short-side tip of Dylan Samberg’s shot with Gabriel Vilardi providing the screen.
"You look at our goal, we got traffic in front of Vasilevskiy with a high tip and he didn’t see it, and that has to be a constant," Winnipeg coach Scott Arniel said. "It was too far between when we did that. We had to do it on a consistent basis."
Gourde pushed the Lightning lead to 3-1 at 15:17. He scored from between the circles by redirecting a quick centering pass from Kucherov.