Lecavalier has a career-high 37 goals this season, five shy of tying Brian Bradley's team record set during the 1992-93 season.
Richards put the Lightning ahead 4-3 with his 20th goal of the season at 1:24 of the third. He has reached the mark in five of his six NHL seasons.
Martin St. Louis had a goal and two assists for the Lightning, who have won 13 of 16. Eric Perrin snapped a 27-game, goal-scoring drought to make it 5-3 with 8:15 left.
Phoenix got goals from Michael Zigomanis, Oleg Saprykin and Derek Morris. The Coyotes are 4-10 in their past 14 games.
Lecavalier put the Lightning ahead 3-2 with a breakaway goal at 15:19 of the first.
Tampa Bay had taken a 2-0 lead eight minutes in on goals by Lecavalier and St. Louis. Goals by Zigomanis and Saprykin tied it midway through the period.
The Coyotes pulled even at three on Morris' first goal in 26 games, scored with 1:44 left in the second.
Saprykin skated slowly off the ice late in the second after blocking a pair of shots with his legs. He returned for the third period.
Notes: Phoenix RW Owen Nolan didn't play due to a sore neck. ... Lecavalier has six goals and 12 points in 11 games against Phoenix. ... Coyotes C Yanic Perreault returned after missing one game with an injured shoulder. ... LW Mathias Tjarnqvist, acquired by Phoenix on Monday from Dallas for Ladislav Nagy, was in the lineup. ... Tampa Bay LW Ruslan Fedotenko has two assists in the third to reach 200 NHL points.