Carolina had three consecutive power plays in the second period but only got four shots on goal.
"Obviously, power play wasn't good enough tonight and that's kind of what hurt us in the second," Hurricanes defenseman Jaccob Slavin said. "We had a lot of chances to even up the game and get the momentum going our way, but we didn't do that tonight."
Shortly after the third penalty kill, Backstrom scored his fifth of the playoffs to make it 2-0 at 14:21, taking a cross-ice pass from Ovechkin on a 2-on-1 and scoring high stick side. It was the Capitals' first 5-on-5 goal since Brooks Orpik's overtime goal in Game 2.
Brett Connolly extended the lead to 3-0 at 16:11 after receiving a pass in slot from Ovechkin, who beat Hurricanes defenseman Dougie Hamilton to a puck behind the net.
"[Ovechkin's] obviously a tremendous player and I just try to get open," Connolly said. "I think his passing is very underrated. Obviously, he's the best goal-scorer arguably of all time, for sure in modern era. I think his passing gets overlooked."
Tom Wilson scored a power-play goal off a rebound in the crease to make it 4-0 at 1:04 of the third period, and Nic Dowd increased the lead to 5-0 on a penalty shot at 8:57.
Ovechkin made it 6-0 at 10:14 with a one-timer off a face-off win by Backstrom on the power play.
"Park it. It stunk," Hurricanes captain Justin Williams said. "There's ups and downs, a lot of momentum swings in playoff series, and we've got to swing it back in our direction in Game 6."