Armia also scored short-handed to give the Canadiens a 2-1 lead at 7:52 with a wrist shot from the left face-off circle.
Brendan Gallagher pushed it to 3-1 at 9:23 when he took a no-look backhand pass from behind the net by Jonathan Drouin and scored glove side before Armia made it 4-1 at 11:15 on a one-timer from above the circles.
"It feels great," Armia said. "I don't know any other way to put it. It feels great and it's a good place to build for the next game."
Nicklas Backstrom scored a power-play goal at 14:27 of the third period to cut it to 4-2.
Armia completed the hat trick with an empty-net goal at 16:58 to make it 5-2.
He has seven goals in his past 14 games after not scoring in his first 26. He has missed 39 games this season, including 19 from Feb. 22-March 31 with an upper respiratory illness.
"He's been through so much this year with his injuries and a lot of bad luck, so we love him and we're really happy to see him get that," Matheson said.
Mike Hoffman scored with 18 seconds remaining for the 6-2 final.
"I think we gave up just too many chances," Strome said. "Just some careless turnovers and not-great reads, and you can't give up two short-handed goals. So, obviously, it's a momentum killer, and kind of leaving Darcy hanging out to dry there, it's not our intention. I think everyone needs to look at themselves and realize we've got to play better.
"Obviously, it's not good enough. We can't be leaving our goalie out to dry. He's bailed us out plenty of times this year so that wasn't good to see."
NOTES:Armia got his first hat trick March 1, 2019, at the New York Rangers. … Washington played 11 forwards and six defensemen after forward Anthony Mantha was a late scratch because of a lower-body injury. There was no update after the game … Strome became the first player to score 20 goals in his first season with the Capitals since T.J. Oshie (26) and Justin Williams (22) in 2015-16. … Suzuki has 63 points (24 goals, 39 assists) in 79 games this season, surpassing his previous high of 61 in 82 games last season. … Matheson, who was plus-4, has 33 points (eight goals, 25 assists) in 45 games this season, surpassing his career high of 31 in 74 games last season. … Kuemper is 0-4-1 in his past five starts. … Washington defenseman John Carlson was minus-4 in 24:18 of ice time.