Alex Ovechkin netted the game-winner at 13:34 in the third period as the Capitals (37-12-6) matched their longest winning streak, set in 1984.
"We don't want to stop. We want to keep winning and playing well," Ovechkin told reporters. "We were frustrated (today) as to how we started the third period but we didn't give up. It's fun when you score game-winning goals."
Playing the team responsible for their last defeat, a 7-4 loss on January 12 in Tampa Bay, Washington took a 2-0 lead with second-period goals from Nicklas Backstrom and Brooks Laich.
The Lightning (22-21-11) rallied in the third, where Martin St Louis scored five minutes into the period and Steven Stamkos tied the game with his 29th goal of the year at 7:42.
After his shaky start, Tampa Bay goaltender Mike Smith settled in and finished with 28 saves but could not hold off the NHL's top offense. The Lightning have lost two straight.
Leaders of the Eastern Conference, the Capitals moved within a point of the top mark in the league. They have dominated of late with high scoring while pulling away in the Southeast Division.
It was a tight one against the Lightning, however, and Ovechkin came to the rescue with his 35th goal of the year. The reigning two-time MVP took six shots and also added an assist.
"The playoffs are like this... you're going to have to win by one or two goals and its going to be tight, so it's good to know we can do that," said Caps defenseman Tyler Sloan.
The team's defense was playing without Mike Green, suspended three games for an elbow against the Florida Panthers Friday.
The Capitals will have the opportunity to set a new franchise mark for successive wins when they visit the Boston Bruins Tuesday.
(Writing by Jahmal Corner in Los Angeles; Editing by John O'Brien)