Kucherov, who had a goal and three assists in a 5-1 win against the New Jersey Devils on Monday, has 24 points (five goals, 19 assists) in his 10-game point streak.
The Lightning have won their past 12 regular-season games against the Red Wings.
Detroit, which has lost four of six (2-3-1), will be missing two of its top goal scorers. Forward Anthony Mantha is out 4-6 weeks with a hand injury sustained against the Colorado Avalanche on Sunday, and forward Tyler Bertuzzi was suspended two games for roughing/instigating against Avalanche forward Matt Calvert.
Tampa Bay has won three straight and six of its past seven to become the first team to 20 wins.