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.
'How to Train Your Dragon 2' releases 5-minute clip
Lytro unveils camera that can focus a photo after shooting it