Jason Chimera and Andre Burakovsky had goals; defenseman Matt Niskanen had two assists and Braden Holtby made 32 saves. He is 22-1-2 in his past 25 decisions.
"We're working hard, all four lines. That's why were successful," Backstrom said.
Rookie left wing Kerby Rychel got his first NHL goal for Columbus (17-26-4) and assisted defenseman Ryan Murray's fourth of the season at 5:07 of the third period to pull the Blue Jackets to within 5-3 but Marcus Johansson scored his 13th of the season into an empty net with 33 seconds remaining.
Boone Jenner had a power-play goal for the Blue Jackets, and defenseman Seth Jones had two assists.
"We played the way we needed to, we wanted to," Jenner said. "They're a dangerous team. We had some breakdowns and give them chances and they capitalized on them."
The Capitals, playing for the fourth time in six days, were outplayed by Columbus (17-26-4) in the first period but skated off with a 2-1 lead because of Holtby, who left his previous start against the New York Rangers on Sunday with dehydration.
"Obviously we didn't have a very good start, they outshot us 10-1 or something," Ovechkin said. "They're a pretty good team. They're working hard especially in the offensive zone.
"That's why we have the best goalie in the League right now. He made some saves and gave us a chance to bounce back."
Five minutes into the second period the Capitals had been outshot 16-9 but led 4-1 against Bobrovsky, playing for the first time in 17 games since sustaining a groin injury on Dec. 8. Bobrovsky finished with 22 saves.
A double minor for high-sticking to Blue Jackets defenseman Justin Falk led to two Washington goals in a span of 1:31 early in the second period to make it 4-1.
Ovechkin scored from the left circle off a pass from Kuznetsov at 3:13, just 13 seconds after Falk was penalized. Backstrom scored his second of the game and 15th of the season at 4:47 when he redirected a feed by Kuznetsov past Bobrovsky.
"We were a little bit slow the first shift in the second period then we got the power play," Washington coach Barry Trotz said. "Our power play sets the tone on the road. There were some positives but you could tell we were tired."
Jenner tied his NHL high with his 16th goal, on the power play at 9:35 of the second, but Bobrovsky's glove failed him on a long wrister by Burakovsky 50 seconds later that made it 5-2.
"We did some very good things 5-on-5, but the mistakes were big mistakes," Columbus coach John Tortorella said. "A couple of turnovers and they buried them.
"Every mistake we made they capitalized. That's why they're the best team in the League. We have to stay within ourselves in those situations and we'll get through it. "
A positive for Columbus was Rychel's goal at 9:30 of the first when he finished off a 2-on-1 with William Karlsson by beating Holtby.
Rychel, the 19th player taken in the 2013 NHL Draft, is on his fifth recall from Lake Erie of the American Hockey League and is playing because several forwards are injured.
"I guess this is my chance to hopefully stick," he said. "I wasn't really too happy with my play the last game. I knew this was my chance to be up here. I really took it and wanted to have a good game and get noticed."
