Ovechkin increased his NHL-leading total to 26 goals and became Washington's career leader in power-play goals, scoring twice with the extra man to pass Peter Bondra, who had 137.
Nicklas Backstrom had a goal and four assists, and Troy Brouwer beat Tampa Bay goalie Ben Bishop in the fifth round of the shootout to provide the Capitals with their fifth win in six games.
Martin St. Louis and Tyler Johnson each had a goal and two assists for the Lightning, who squandered a three-goal lead in losing their sixth straight at Washington.
Brad Boyes scored the winning goal in a shootout as the Florida Panthers defeated the Detroit Red Wings 3-2.
Aleksander Barkov also scored in the tiebreaker for Florida to make it three wins of four overall and two in a row against the Red Wings.
Tomas Tatar scored for Detroit in the shootout but Tim Thomas stopped shots by Daniel Alfredsson and Gustav Nyquist.
The Nashville Predators ended a five-game losing streak with a 4-1 win over the New York Rangers as Nick Spaling and Rich Clune scored first-period goals and seldom-used backup Carter Hutton made 28 saves.
The Buffalo Sabres beat the Ottawa Senators 2-1 in a shootout, Zemgus Girgensons scoring the tying goal in the second period and adding a score in the 10th round of the shootout. Buffalo went to 4-0 in games decided by a shootout, while Ottawa fell to 0-5.
Nick Foligno scored the game-winning goal with 91 seconds left when Ryan Johansen's shot went in off his skate as the Columbus Blue Jackets defeated the New Jersey Devils 5-4.
Rookie goalie Martin Jones made 31 saves for his second shutout in two games as Jordan Nolan, Anze Kopitar, Alec Martinez, Tyler Toffoli, Jake Muzzin and Justin Williams scored for the Los Angeles Kings in the 6-0 win against the Montreal Canadiens.
The Chicago Blackhawks cruised to a 6-2 win over the Dallas Stars, Patrick Sharp scoring twice.
The Phoenix Coyotes won 3-1 against the Colorado Avalanche with Antoine Vermette scoring two goals and Thomas Greiss stopping 29 shots.
Boston beat Calgary 2-1, Edmonton edged Carolina 5-4 and the New York Islanders won 3-2 over San Jose in a shootout.