The Senators got off to a rough start in the first period as Ward opened the scoring on Washington's second shot of the game just 2:11 in. Ward's shot hit Anderson's stick and caromed into the net.
After that, Anderson played his best game of the season. He cited the Senators' penalty-killing, shot blocking, and play along the boards as keys to the victory.
"It's stuff that doesn't always show up on the score sheet like goals and assists do," he said. "It's those little things that make a difference in a game, and a lot of people don't realize that, but we definitely recognize it in the room."
Ottawa tied it at 13:49 of the first when Zibanejad and Cory Conacher put together a great passing play. They broke in on a 2-on-1 rush, and completed a give-and-go that finished with a tap-in by Zibanejad.
Ottawa lost forward Chris Neil midway through the first period when he collided with Ovechkin. Neil was sidelined by a lower-body injury.
Senators coach Paul MacLean said it will likely sideline Neil for a bit. Neil will need to undergo further evaluation before it is known how long he will be out of action.
Ovechkin said he took the worst of the collision, and believes the NHL should review the play that went unpenalized.
"I think four guys out there didn't do their job. I think they started celebrating New Year's too early, right before the game," Ovechkin said. "They didn't see headshots on Neil against me.
"I felt like he was going to hit me shoulder to shoulder. I was ready for it, but he hit right in my head, right in my chin."
NOTES: Ottawa C Jason Spezza and D Chris Phillips missed their second straight game because of lower-body injuries. D Eric Gryba was a healthy scratch. ... The Capitals are dealing with trade demands from a number of players, including G Michael Neuvirth, who was a healthy scratch. ... Washington C Brooks Laich missed his third straight game because of a strained groin. D Alexander Urbom was a healthy scratch.