Kucherov, who recorded his 600th NHL assist in the second period, extended his point streak to eight games (four goals, 10 assists).
"Cool," Kucherov said about his milestone.
Said Tampa Bay goalie Andrei Vasilevskiy of Kucherov: "Obviously he's one of the greatest to play for this team. An exceptional player and one of the biggest reasons we've had success over the past few years."
Darren Raddysh had a goal and an assist, and Brayden Point also scored for the Lightning (25-16-3), who have won five of seven (5-1-1). Vasilevskiy made 39 saves.
"Well, he's been consistent the whole year," Kucherov said of Vasilevskiy. "He's been our best player, and we've got to play better in front of him."
Lucas Raymond scored for the Red Wings (21-20-4), who had won eight of nine. Cam Talbot allowed five goals on 16 shots before being replaced by Alex Lyon to start the third period. Lyon stopped all six shots he faced in relief.
"They owned us in and around our blue paint and I didn't think we were real aggressive around their blue paint," Detroit coach Todd McLellan said. "Yeah, we had 40-some shots on goal, but Vasilevskiy saw most of them and I don't think we did a lot to help our goaltenders around the blue paint."
Point gave Tampa Bay a 1-0 lead at 2:02 of the first period when he scored on a rebound of Emil Lilleberg’s shot that deflected off the end boards.