Dryden Hunt, Filip Chytil and Alexis Lafreniere scored for the Rangers, who ended a three-game losing streak. Kaapo Kakko and Braden Schneider each had two assists, and Alexandar Georgiev made 34 saves.
"I'm glad we finished on a strong note because we deserved that," Gallant said. "We had a good year. The team played really well and to get 110 points is an accomplishment, and they should be proud of that."
John Carlson and Justin Schultz scored, and Ilya Samsonov made 30 saves for the Capitals.
"We're going to have to reach back and do more," Carlson said. "Whatever it is leading up to the playoffs, you want to get into as good a position as you can, you want to feel good about your game individually and as a team. I think over the last month or so we've played some of our best hockey all year. With that said I think we're a confident group. We know what we have in there and what we're capable of, and now it's go time."
Hunt gave New York a 3-2 lead at 6:44 of the third period. He got the puck in the right face-off circle from Kakko, made a move around Samsonov's outstretched left leg and tucked it inside the right post.
"Kaapo just made a great play and I kind of ran out of room, and then I got lucky that there was that little opening," Hunt said. "I'll take that."
Chytil gave the Rangers a 1-0 lead at 3:26 of the second period.