Washington won its fifth straight and increased its lead over second-place Carolina to 12 points in the Southeast Division.
Chris Clark, however, made it a 6-4 game with 7:13 to play and Ovechkin scored his 26th of the season with 1:46 to go.
The goals by Collins and Clark were their first of the season. Collins was recently called up from the minors and Clark has been out for more than a month with a forearm injury.
All seven Washington goals were scored against Mike Smith, who made 28 saves -- and who had come into the game with a goals-against average of 2.42.
Brent Johnson stopped 21 shots to get the win.
Vincent Lecavalier scored twice in the second period for Tampa Bay, which lost its second straight.