Bunting tied it 1-1 at 1:29 of the second period with a power-play goal. He jammed in a loose puck at the top of the crease after Tavares deflected Mitchell Marner's shot from the top of the right circle.
Morgan Rielly put Toronto ahead 2-1 at 7:00 when he collected a loose puck in the slot after Bunting put it in front from behind the net. It was Rielly's first goal this season (36th game).
"Just relief. It felt good," Rielly said.
Tavares said Rielly had not let the goal drought affect his demeanor around the team.
"I don't know if I've ever played with a better professional than Morgan," Tavares said. "The way he carries himself, you'd never know (he hadn't scored). I think he is a world-class player, person and leader, and when the puck hasn't been going in, it's never easy especially between the ears. ... You don't see him hanging his head or sinking his shoulders."
William Nylander made it 3-1 at 10:45 when he jammed in a loose puck at the top of the crease after Calle Jarnkrok's shot on a 3-on-1 produced a rebound.
Pierre Engvall extended the lead to 4-1 at 14:20. He received a pass from TJ Brodie, skated into the high slot, and shot glove side.
"I thought the first period was good, the second period, we didn't do the right things defensively, and it burned us," Washington coach Peter Laviolette said.
"It was out of position, wrong assignment, and it caught us. I don't think it was an overwhelming amount of pressure, but at the end of the day, it's about details, and I think the details in the second period were not good enough."