Rodrigues scored his second of the game with a one-timer from the left point, cutting it to 5-3 at 15:57.
"It was a bit of a messy game in a lot of ways," Pittsburgh defenseman Mike Matheson said. "There were some breakdowns in coverage on both sides. I think from our perspective, that definitely wasn't good enough. I think at the same time though, to go into that third period down 4-0 and then have it go 5-0, knowing that we have a game tomorrow night with travel, I think it would have been pretty easy for us to go, 'You know, it's not our night.'"
Batherson scored into an empty net with 48 seconds remaining for the 6-3 final.
NOTES: Senators forward Shane Pinto sustained an upper-body injury in the second period and left the game. Pinto had missed the previous nine games with an upper-body injury. Smith said it "doesn't look good." … Batherson had his second four-point game of the season (three goals, one assist against the Washington Capitals, Oct. 25). He is one of four players in the NHL this season with multiple games of at least four points (Leon Draisaitl of the Edmonton Oilers, Tyler Bertuzzi of the Detroit Red Wings, Roman Josi of the Nashville Predators).