Senators forward Kyle Turris wristed a shot over Jeff Zatkoff's glove in the first round of the tiebreaker, and Jason Spezza ended the game when he beat Zatkoff with a backhander in the second round. Robin Lehner stopped Pittsburgh's Beau Bennett and Jussi Jokinen.
Lehner also made 26 saves through 65 minutes to earn his 12th win of the season. The Senators did not qualify for the Stanley Cup Playoffs but did finish the season on a five-game winning streak, which Spezza said allows them to enter the offseason on a positive note.
"It's a nice way for us to finish. We won a lot of games at the end even though they didn't mean anything, but it showed we were playing for each other," Spezza said. "It's hard to play a back-to-back and a game that doesn't mean very much, but I thought we battled hard and it was a good feeling to end on a winning note."
The Penguins, the Eastern Conference's second seed as the winner of the Metropolitan Division, will play the Columbus Blue Jackets in the playoffs. Their Eastern Conference First Round series begins Wednesday.
Pittsburgh finished with 109 points, the second-highest single-season total in franchise history, but coach Dan Bylsma said that will not mean much if the Penguins do not play well in the playoffs.
"You can talk about the number of wins and the number of points and ranks in Penguin history, but really that's just given us our spot in the playoffs," Bylsma said. "That's what we know. That's where we're going to be and our success will be measured in playoff wins."
Pittsburgh captain Sidney Crosby didn't dress for the game but still captured the second NHL scoring title of his career. Crosby finished the season with 104 points.
The Senators (37-31-14) finished five points behind the Detroit Red Wings, the second wild-card team in the East.
"I think one thing we have to do is we have to go into training camp and start at square one and go from there," Senators coach Paul MacLean said. "This is really a moral victory, the last five games we played and being able to find ways to win. We have work to do and we have to come to training camp in September prepared to do the work and make the changes to our game.
"That's going to make us successful.
The game entered the third period tied 2-2 after the teams traded goals in the second.
Lee Stempniak gave Pittsburgh a 2-1 lead at 5:16 when he tipped a shot from Bennett past Lehner for his fourth goal since joining the Penguins at the NHL Trade Deadline.
Pittsburgh held the lead until Mark Stone scored a power-play goal at 17:14. With Chris Kunitz in the penalty box, Stone collected the rebound of a shot by Patrick Wiercioch and wrapped it around Zatkoff's left pad.
Each team managed two shots through the first 14:27 of the first period, but the game then opened up and each team scored before intermission.
Jokinen opened the scoring with Ottawa's Milan Michalek in the penalty box for hooking. He attempted a pass to James Neal that deflected off Senators defenseman Eric Gryba's skate and through Lehner's five-hole at 14:46.
Turris answered at 18:38 when he slapped a shot past Zatkoff with one second left on a penalty to Pittsburgh forward Harry Zolnierczyk to tie the game at 1-1.
The Penguins finished the season with more than 500 man-games lost to injury, but have started to get some players back in the lineup. Jokinen said the return of players such as defensemen Kris Letang and Paul Martin will be pivotal in the postseason.
"That's really important. We've been battling through a lot of injuries to a lot of our key guys," Jokinen said. "I think during the playoffs we're going to need our depth, for sure. We showed during the regular season we have depth and every guy has to do their roles and be ready to jump in when they are playing."