Gibson, who is 3-0-1 in his past four starts, got his 163rd win to pass Jonas Hiller for third place in Ducks history (Jean-Sebastien Giguere, 206; Guy Hebert, 173).
"I always hold myself to high expectations," Gibson said. "I've been playing well and finding ways to win, and that's all that matters right now."
Troy Terry and Rickard Rakell scored for Anaheim (23-16-8), which is 4-0-1 in its past five games.
Gibson saved all 34 shots he faced in the final two periods. He is 15-10-7 with a .922 save percentage in 32 games this season, his ninth with Anaheim.
"[He] should be right at the top of the (Vezina Trophy) list," Ducks defenseman Cam Fowler said of voting for the top goalie in the NHL. "He's been incredible, so right up there with any goaltender in the league."
Tyler Ennis scored, and Anton Forsberg made 18 saves for Ottawa (13-21-4), who had their four-game point streak end (2-0-2).
"Their goalie put a clinic on," Senators coach D.J. Smith said. "You can come up with reasons why you don't score or come up with different excuses. We had 45 shots and plenty of good looks, so he's the difference."
Terry made it 2-1 at 3:42 of the third period with a wrist shot on a 1-on-1.
"We've talked about it a lot in our room, but you can see how dangerous Troy Terry is," Ducks assistant Geoff Ward said. "You give him that one second and he can make a difference in a hockey game. And tonight he did."