Alexander Semin came up big for the Caps for the second consecutive night, tying the game 1-1 with 5:32 remaining in the third period.
Goalie Braden Holtby replaced Michal Neuvirth after the opening period and stopped 21 shots before stopping Dominic Moore, Adam Hall and Vincent Lecavalier in the shootout.
Sean Bergenheim scored Tampa Bay's goal on a first-period power play, redirecting a shot past Neuvirth. There was no immediate announcement on why Washington's starting goalie left the game.
Semin scored the winning goal in Washington's 3-2 overtime victory at Florida on Sunday night. That carried the Capitals past the Lightning into first place in the Southeast Division.
CANUCKS: Vancouver recalled forward Victor Oreskovich from Manitoba of the American Hockey League after losing Mason Raymond to an apparent shoulder injury Sunday.
If Raymond can't play today in Phoenix, the Canucks might be short a forward. Chris Higgins is out with a broken thumb.
The 24-year-old Oreskovich had one assist in eight games on Vancouver's fourth line this season.