Claude Giroux and Alex DeBrincat also scored, Shane Pinto had a pair of assists and Cam Talbot made 27 saves for the Senators, who snapped a two-game losing streak.
Yakov Trenin and Nino Niederreiter scored and Juuse Saros made 30 saves for Nashville, losers of two straight.
Batherson and Niederreiter scored goals a minute apart in the third. Batherson's came with the teams skating 4-on-4 just as a DeBrincat penalty expired, giving Batherson credit for a power-play goal.
''It was nice that to see one go in obviously at that point in the game, just super fired up,'' Batherson said. ''I lost an edge right before that and I was able to sneak behind the D and able to squeak one in. I'll take it.''
Niederreiter's goal made it 3-2 with 9:45 remaining, but the Predators could not find the equalizer.
Trenin scored the game's first goal at 16:57 of the second period after Mark Jankowski jarred the puck loose just inside the Ottawa zone and found a trailing Trenin, who beat Talbot with a wrist shot on the far side.
''I think we were in total control for 40 minutes of the game, and then we made some mistakes, which we made consistently already,'' Trenin said. ''Once we fix those, we going to be a better team.''
Giroux sent the teams to the second intermission tied at 1 with a power-play goal with 7.5 seconds remaining. Nashville was shorthanded due to a too many men on the ice penalty, then Predators defenseman Jeremy Lauzon was jammed into the boards by Ottawa's Mark Kastelic. Lauzon skated directly to the Nashville bench, but a replacement was unable to get back into the play before Giroux swatted the puck home after a scramble in front.
''Give Kastelic a lot of credit there,'' Ottawa coach D.J. Smith said. ''He puts that guy into the boards. I think it's a clean play and he's standing on the goalie. He's giving us everything he's got.''
DeBrincat was credited with giving Ottawa the lead at 3:55 of the third when he attempted to pass the puck to Batherson, but it deflected off of the stick of Predators defenseman Dante Fabbro and between Saros' pads.
''Yeah, those are always tough, but I think I got to find a way to get it out of there,'' Fabbro said. ''Intercepted the pass and just off my stick.''
Nashville played the third period with just four defensemen. Lauzon did not return for the third period, and Alexandre Carrier did not play after the five-minute mark of the second. He logged just 12 shifts in the game and 7:20 of ice time.
Predators coach John Hynes did not have an update on either player following the game.
HOT POWER PLAY
Despite coming up empty with the man advantage in three attempts with the man advantage at Dallas on Thursday, Ottawa's power play entered Saturday with six power-play goals in their last 16 opportunities. With two power-play goals in six chances Saturday, the Senators have found the back of the net in eight of their last 22 chances.
Five minutes into the second period, there was a tense moment on the Ottawa bench when a frustrated Thomas Chabot tried to slam his stick against the glass between the benches. Unfortunately for fellow Senators defenseman Travis Hamonic, Chabot's stick caught him just under his left eye, causing him to fall backwards on the bench.
Hamonic was tended to by Ottawa's training staff and an apologetic Chabot, and remained on the bench and did not miss a shift.
Predators: Visit the St. Louis Blues on Monday.
Senators: Host the Anaheim Ducks on Monday.
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