Richards, who had a goal and two assists, wasted no time in feeding St. Louis on the right side. St. Louis wristed a shot over the stick side of Jeff Hackett for his team-leading 17th goal.
Tampa Bay ended a six-game road winless streak and a 1-2
Defenseman Dan Boyle and Richards put the Lightning ahead, 2-1, after Chad Kilger scored the only goal of the first period. Richard Zednik directed the puck to Koivu behind the net and the Canadiens' captain fed Kilger in the slot for the goal.
Zednik picked up assists on both Montreal goals as that line accounted for all six points.
Boyle scored his third goal in the last two games, giving him 12 points in his last 10 contests. Richards also has produced of late, with three goals and nine assists in the past eight games.
Khabibulin stopped 18 shots for just his third win in his last 11 starts after beginning the season at 7