"If you look at most of my goals, I'm not the kind of guy that's going to score from outside the circle," St. Louis said. "It's just not my game. I try to get free and go to the net. That's what I did tonight, and the puck came to me."
Ottawa, which has dropped seven of 10, got a goal from Patrick Wiercioch.
"We're just finding ways to lose," Wiercioch said. "We know we can be a better team and be more consistent, and we haven't proven that yet."
Lightning coach Jon Cooper said Aulie will have surgery Friday and that Hedman likely will miss Saturday night's game against Winnipeg.
"I don't know when he's coming back," Cooper said of Hedman. "He's more a day to day. We'll see what happens, but I don't expect him back for Winnipeg."
The Lightning were already without several key players, including center Steven Stamkos (broken leg), left wing Ryan Malone (broken ankle), and defensemen Eric Brewer (lower body) and Radko Gudas (upper body).
"A big effort from an extremely short-handed team," Cooper said.
Stamkos has a goal of returning in February, while Malone will be out three to four weeks. Brewer and Gudas could soon return.
St. Louis beat goalie Robin Lehner from just outside the crease to give Tampa Bay a 2-1 advantage 13:19 into the second. The Lightning captain tied Jason Arnott for 91st place on the NHL points list with 938.
Filppula's goal from the left circle made it 3-1 at 10:56 of the third.
St. Louis put the Lightning up 1-0 when he scored while falling forward with 3:15 left in the first.
Wiercioch tied it at 1-all with a power-play goal 6:11 into the second. The defenseman had not scored a goal in his previous 20 games dating to last season.
"Obviously, we didn't play hard enough to win," Ottawa coach Paul MacLean said. "I don't think it's like inches and inches and miles and miles that we have to play harder, but we have to play harder longer."
Bishop made one of his 33 saves early in the first on Chris Neil's slot shot. The Lightning acquired Bishop from Ottawa last April.
"It's always nice to beat a team that traded you," said Bishop, who has won both of his games against the Senators.
Lehner kept the Senators within one early in the third when he stopped a shot by Nate Thompson during a breakaway. Lehner finished with 19 saves.
"We were just not good enough," Senators captain Jason Spezza said. "I think we were playing too cautious, and in turn I don't think we played with enough confidence and made too many mistakes. It just seemed like we were a little bit scared to make mistakes, and when you play cautious like that and don't play with enough confidence, that's why we're losing games. We have to be a more attacking team. We have to believe in ourselves more than we do."
St. Louis was held pointless in his previous three games. ... Ottawa C Kyle Turris had an assist, and has seven assists and 12 points in 10 games against Tampa Bay.