Oshie completed the feat with an empty-net goal during the 4-2 victory.
Nicklas Backstrom was one of the first players to share the moment with Oshie.
"I felt like he needed a hug," Backstrom said, according to the Washington Post's Samantha Pell. "I think I told him, 'You're the strongest person I know.'"
Oshie was visibly emotional on the bench afterward.
"We are trying to be there for him and take care of him, and he ends up taking care of us," Nic Dowd said.
Oshie previously delivered a memorable interview after winning the Stanley Cup in 2018, which his father was able to attend in person.
With the hat trick, Oshie now has 21 goals and 21 assists in 51 games this season.