A seventh straight defeat on Saturday would tie a franchise record that dates back to 1935.
After the Habs took a 1-0 lead on Alex Kovalev's 13th goal of the season, Vincent Lecavalier and Andre Roy put Tampa ahead 2-1.
Tomas Plekanec managed to tie the at 2-2 with just over five minutes to play, but the Lightning ultimately triumphed in the shootout when Brad Richards laced a shot over Carey Price's right shoulder.
Marc Denis was in net for Tampa, and blocked a Saku Koivu attempt to win his first game of the season.
If the Canadiens have any pride left, they'll play a desperate game against the Toronto Maple Leafs on Saturday to avoid making the wrong kind of history.
(Picture: Canadian Press)