Backstrom had an assist, and Anthony Mantha scored his second goal in as many games with the Capitals (28-12-4), who had won three straight. Vitek Vanecek was pulled after allowing four goals on 21 shots. Craig Anderson made eight saves in relief.
"I think we were lacking a little bit of compete level and poor decision-making at times just cost us today," Washington forward Lars Eller said.
The Capitals remained in first place in the eight-team MassMutual East Division, two points ahead of the New York Islanders, who lost to the Boston Bruins 4-1.
Tokarski's last win was Dec. 12, 2015, when he made 25 saves for the Montreal Canadiens to defeat the Ottawa Senators 3-1. He pointed to the rafters when the final horn sounded and his teammates came to congratulate him.
"It's pretty incredible, to be honest," the 31-year-old said. "I lost my dad a few years back, so that was the first NHL win since he's passed, so I was just pointing up to him for that special moment. And then all the guys were just awesome coming in. There's nothing better for a goalie than celebrating with your teammates after a win."
The Sabres took a 1-0 lead at 18:50 of the first period when Dylan Cozens' shot from the point was deflected midair by Reinhart.
Dmitry Orlov tied it 1-1 at 19:37. After Tokarski saved Orlov's shot from the point, T.J. Oshie controlled the rebound and passed back to the defenseman.
Victor Olofsson gave the Sabres a 2-1 lead at 1:36 of the second period when he stole an errant pass near the Capitals blue line and scored with a wrist shot from the right circle.
Washington turned over the puck 15 times.
"Turnovers played a huge factor in it," Capitals coach Peter Laviolette said. "A lot of times you turn the puck over because you're not moving the way you're capable of moving. Your strides, you're on your toes, and they were on their toes tonight. They were forcing the issue."
The lead was 3-1 after Casey Mittelstadt came in on a break and beat Vanecek for a shorthanded goal at 5:42.
"'Bjorky' made a nice play, just tipped it up to me," Mittelstadt said. "I actually kind of thought Bjorky would be with me, so I slowed down and looked back a little bit and he wasn't there. It was one of those plays where it almost happened so quick, and you just look up and see a little bit of netting and just fire it, and sometimes it works out better than when you're thinking about it and looking for a longer time."
The Capitals got within 3-2 during a delayed penalty when Mantha shoveled a cross-ice feed from John Carlson past Tokarski at 9:59. Mantha was traded by the Detroit Red Wings on Monday and had a goal and an assist in his Capitals debut Tuesday, a 6-1 win against the Philadelphia Flyers.
