Brayden Point extended the lead to 2-0 at 2:26 of the third when he scored from the edge of the crease to finish a give-and-go with Kucherov.
"I thought we, as a group, played pretty hard, played pretty well, probably deserved more than the scoreboard showed," Washington forward Tom Wilson said. "But that's hockey sometimes. We've got to find a way to kind of crack it open in those games when there's not much of anything going on."
Geekie made it 3-0 at 3:10 with a one-timer from the left face-off circle off a pass by Anthony Cirelli.
"[Brandon Hagel] is a great guy, Tony too. They make it easy on you," said Geekie, who was playing his eighth NHL game. "It makes it a lot easier coming to the rink when you are playing with those two. Hopefully more to come. For now, I think it’s just keep putting in the work, and hopefully we can keep it going."
NOTES: Kucherov has 14 points (eight goals, six assists) during his point streak, which is tied with former teammate Steven Stamkos (2012-13) for the second-longest streak to begin a season in Lightning history. The record is 11 games, held by Kucherov (2017-18), Stamkos (2017-18) and Martin St. Louis (2009-10). ... The Lightning’s previous shutout of the Capitals was April 13, 2014, a 1-0 shootout victory.