Mattias Ekholm had three assists and Alexandre Carrier two assists for the Predators.
Brady Tkachuk scored, and Anton Forsberg made 28 saves for the Senators (23-37-6), who played one night after the death of owner Eugene Melnyk. Ottawa is 2-6-1 in its past nine games.
"Super proud of the guys," Senators forward Austin Watson said. "First and foremost, just a sad day for our organization. I didn't get a chance to spend any time with Mr. Melnyk, but he was a guy that was committed to our hockey team.
"He was passionate about Ottawa, the Senators, and the community when it came to the game and bringing it to Ottawa. It's a tough day, obviously tough for his family. So condolences and prayers go out to them. It was great to see the guys move forward and put a good effort."
Tkachuk scored at 4:53 of the first period to make it 1-0. He redirected Tim Stutzle's pass across the crease during a 5-on-3 power play.
McCarron tied it 1-1 at 19:21 of the first on a shorthanded goal. Forsberg skated behind the goal line to clear a puck that never reached the trapezoid. McCarron collected the loose puck and scored on a wraparound.
The Predators took five of their six minor penalties in the first period.
"I think we took three penalties in the first five minutes, [and we were] down 5-on-3," Nashville coach John Hynes said. "That's tough sledding right off the bat. I thought that was an issue in tonight's game overall with the amount of penalties we took, and back-to-back penalties."
McCarron's second goal made it 2-1 at 18:14 of the second period. Ekholm sent a pass from the sideboards to the top of the crease, and McCarron slid the puck between Forsberg's legs.
Saros made a save on Connor Brown's penalty shot with 7.2 seconds left in the second, after defenseman Roman Josi was called for slashing Brown during a breakaway attempt.
"I think [Saros] took some of our confidence away with the saves he made," Ottawa coach D.J. Smith said. "In the first and second power plays, some of those backdoor plays, those are big-time saves. But we've got to find ways to score. One goal is not going to do it. But also we can't leave guys wide open in front of the net or we've got to be harder in front of our net."