Pekka Rinne made 25 saves for the Predators (20-10-1), who had lost two in a row. They are in first place in the Western Conference with 41 points and are 9-0-0 against Eastern Conference opponents.
"I thought that defensively we did a really good job," Rinne said. "They didn't have much of anything all night. Just a solid defensive game]. I mean, we needed that win. You could tell."
***[WATCH: [All Senators vs. Predators highlights]*
Zack Smith scored for the Senators (13-15-4), who are 1-3-1 in their past five games and have scored two goals or fewer in five consecutive games. Craig Anderson made 33 saves.
"We're missing six guys and I thought the guys gave everything they had," Ottawa coach Guy Boucher said. "You could see that they were the older, more mature team, and when they got their push it was hard for us to keep up with that push. The guys fought, but we needed to get that second goal there earlier and keep it tighter."
Jean-Gabriel Pageau (Achilles), Mark Borowiecki (upper body), Matt Duchene (groin), Bobby Ryan (concussion), Christian Jaros (lower body) and Dylan DeMelo (upper body) missed the game for the Senators because of injury.
Ellis gave the Predators a 2-1 lead at 9:01 of the second period on a one-timer from the slot. He started a give-and-go with Roman Josi and scored his third goal.
"It's more just read and react," Ellis said. "I mean, we've been playing together here for a while and [Josi] is so mobile, so if I can get moving it helps him out and vice versa. We try to create as much space as we can for each other and see what happens when we do."