The pressure-free 4-0 victory came in the Capitals' first home game since being mathematically eliminated from Stanley Cup Playoff contention two days earlier. Washington will miss the playoffs for the time since 2007.
"I told the guys when we found out it was over that part of their job as a professional is to play as hard as you can," coach Adam Oates said. "Do it for yourselves and do it for the people who paid to come watch you play. You owe them."
"We talked about it as soon as we found out our chances were gone for the playoffs," Beagle said. "We had talked about it a couple of times as a group, as a team. We just said let's finish hard, let's finish strong and be professionals and do it for our fans. And win for ourselves, too."
Goaltender Jaroslav Halak stopped 34 shots for his fifth shutout of the season and 30th of his career.
The Blackhawks, without star forwards Patrick Kane and Jonathan Toews due to injury and with defenseman Duncan Keith receiving a night off, had little to play for and saw their four-game winning streak end. Chicago is locked in as the third seed in the Central Division and will open the playoffs on the road against the Colorado Avalanche or St. Louis Blues.
"It doesn't matter what's on the line, it's important that we show up and play, wearing the [Blackhawks] jersey," forward Patrick Sharp said. "It doesn't matter who's playing or who's not playing, you want to go out there and work your hardest and play your best. We clearly didn't do that.
"It's the NHL. We're professionals and we should be ready to go. But we can't start the game like that and spot them a lead like that."
The Blackhawks close their regular season Saturday on the road against the Nashville Predators.
Ovechkin, who is all but assured of winning the Maurice "Rocket" Richard Trophy for the fourth time in his career, padded his goal-scoring lead on the power play 2:04 into the game to give Washington an early 1-0 lead. From his usual place inside the left circle, Ovechkin unleashed a one-timer that blew past Corey Crawford (16 saves) for his 51st goal of the season.
Beagle extended Washington's advantage to 2-0 at 9:22. After receiving a pass from Evgeny Kuznetsov, Dmitry Orlov noticed Beagle lurking backdoor. His pass hit Blackhawks defenseman Nick Leddy on the way, but Beagle was still able to corral the puck and push it past Crawford.
"It was a tough start," Blackhawks coach Joel Quennevile said. "They score like that from there and they get an early one like that in the second. Both periods we lose whatever energy we were looking to get in a game like that. It's one of those nights where [the Capitals] were clearly the better team."
The Capitals doubled their lead in the second period. Backstrom scored his 18th of the season on a sharp-angled shot from along the goal line that banked off Crawford and into the net at 1:19.
Beagle scored his second of the game and fourth of the season at 16:16. After the Capitals worked the puck along the end boards, Beagle finished Jason Chimera's centering pass. It marked the first multi-goal game of the 28-year-old forward's career.
"[Orlov] made a great pass to me on that first one and then [Chimera] made a great backhand pass to me," Beagle said. "It almost surprised me in the slot, that it came out to me that fast and that crisp. Trying for the third one, the guys were hitting me no matter where I was. It was a fun game to be a part of."
As the game ended, Beagle's teammates did whatever they could to give him an opportunity for the hat trick.
"We were fired up," defenseman Karl Alzner said. "We didn't even want to let him off the ice at the end there, but he was gassed so we had to. If you go around the room, he's the guy that people rally around the most. We get the most fired up when he does well. It was awesome. I'm really happy for him. Everyone else is too."
Antti Raanta replaced Crawford to start the third period and stopped all seven shots he faced.
"It feels like everything was just working for them," Crawford said. "In this game, everything worked and they created some good opportunities. I gave them a couple bad ones, but it just felt like everything they did worked, and everything we did didn't."
Washington lost forward Marcus Johansson to an upper-body injury early in the second period after he was struck by a Backstrom shot. He will miss the season finale.