Leino's second goal came with 3:16 left in the game. He went 360 degrees in front of the net to avoid sliding Nashville forward Martin Erat and beat goalie Anders Lindback with a backhand on the high glove side for the winner.
Jeff Carter also scored for the Eastern Conference-leading Flyers in the start of a four-game homestand.
Sergei Bobrovsky had 26 saves for the Flyers.
Marcel Goc and Joel Ward scored for the Predators.
The Flyers won on the night they honored Hall of Famer and their former captain, Bobby Clarke.
They surely made the Stanley Cup champion happy on this night.
Leino scored a power-play goal for his 12th of the season early in the third for a 2-1 lead. He sneaked in a rebound from a side angle for the tough goal, the start of his first two-goal game of the season.
With All-Star Claude Giroux in the penalty box for high sticking, Ward took advantage and slammed in the rebound from the slot for the power-play goal that tied the game at 2-2.
The Predators held their annual fathers' trip at the game and the road-tripping dads enjoying the game from the luxury box erupted in cheers at the goal.
The Predators wouldn't beat Bobrovsky - known in the locker room simply as "Bob" - again.
Bobrovsky was pulled after allowing three goals on six shots during the first period against the Lightening. He rebounded with an outstanding effort, stopping all 13 shots in the second period.
The Flyers haven't lost consecutive games since Dec. 20 and Dec. 28.
The Flyers were shutout against Tampa Bay in their first game back from the All-Star break, a listless start to the second half after they entered the break atop the NHL standings.
The Flyers entered with a league-best 173 goals and ended any thought of consecutive shutout losses when Carter's wrister from the circle for his 24th goal late in the first gave them the early lead.
Not for long.
Goc scored his ninth goal of the season 61 seconds later to tie the game - and that's the way it stayed until Leino's first goal.
The Predators briefly thought they went up 2-1 on Goc's second goal only to have it waved off because of incidental contact.
Nashville defenseman Patric Hornqvist lost his balance and backed into Bobrovsky. Nashville coach Barry Trotz fumed as he watched the overhead replay, arguing the contact wasn't severe enough to disallow the second-period goal.
The Flyers celebrated Clarke before the game and presented him with his retired number banner from the Spectrum. He's still the Flyers career leader in assists and points and led them to consecutive Stanley Cup championships in the 1974 and 1975. He works as the Flyers senior vice president and consultant to general manager Paul Holmgren.
Clarke said it's too early to compare this year's Flyers to those old Broad Street Bullies teams.
"It's got pretty much every ingredient you could want," he said. "If they could win the Cup, it would be a great team. Everybody from my era is hoping that they could win the Cup, obviously."
Notes: The Flyers and Predators have made more trades with each other (17) than they have played games against each other (14). ... Clarke doesn't miss the day-the-day of grind of working as the Flyers general manager. He resigned in October 2006. "Not for any other reason than that I don't want to sit behind a desk all day and do those kinds of things. I did it until I had enough," he said. ... Japanese eating champion Takeru Kobayashi was at the game. He'll attend Friday's Wing Bowl and attended the game with the commissioner of the chicken wing eating competition, former Flyers goalie Bernie Parent.