Aube-Kubel put the Capitals ahead 1-0 at 10:22 on a slap shot from the right face-off circle after being recalled from Hershey of the American Hockey League earlier Friday.
Beck Malenstyn made it 2-0 with a wrist shot 15 seconds later at 10:37 for his first goal of the season. Martin Fehervary had an assist on the play, but he left after sustaining a lower-body injury in the second period.
"I thought we were ready from the start, that first shift, Kuznetsov's line with (Alex Ovechkin and Tom Wilson) sort of set the tone right away," Washington coach Spencer Carbery said. "Then Aube-Kubel, Nic Dowd and Malenstyn had a lot of energy on the fourth line.
Dowd returned after missing nine games because of an upper-body injury.
"For the first time this year, we had sort of our natural fourth line, a real identity. It was what we thought our fourth line would look like. So, credit to them. Dowd comes in, and I thought he was excellent."
Kuznetsov extended it to 3-0 at 6:34 of the second period on a snap shot from the slot off a pass from Wilson on a 2-on-0.
"It was a good start, but then we give up a couple goals late in the third, so they were able to come back, but eventually we got the [win]," Kuznetsov said. "That's all that matters. For us, it was very important to get the [win], especially in the first game of the back to back. The coaches will look what went wrong and we're going to fix that part for sure."