Leino made fellow Finn and Stars goaltender Kari Lehtonen look like a fool, moving the puck slightly to the right as the Dallas netminder dove for a poke- check. With a wide-open net in front of him, the second-year player calmly slid the disc home to end the contest.
Jeff Carter and Mike Richards scored in regulation for the Flyers, who won their fourth game in six.
Sergei Bobrovsky got the win with 27 stops as Philadelphia clinched its 15th postseason entrance in the last 16 seasons and pulled two points ahead of idle Washington for the top spot in the Eastern Conference.
The Flyers and Capitals square off in America’s capital on Tuesday.
Alex Goligoski and Stephane Robidas tallied for the Stars, who have dropped three of four but remained firmly entrenched in the Western Conference playoff scene.
Lehtonen fell to 0-10-2 all-time against Philadelphia, suffering the loss despite 28 saves.
The Flyers opened the scoring with 1:21 left in the first period, when a a point drive from Andrej Meszaros was redirected home by Carter.
Richards made it 2-0 just 77 seconds into the second period when he batted a puck out of the air at the left post, but a fluttering Goligoski point shot sailed through traffic and in to get the Stars on the board at 12:44.
Claude Giroux faced a wide-open net with just over seven minutes left in the third period, but he lost control of the shot long enough for the puck to carom off the left post.
Just over a minute later, Bobrovsky sealed off the right pipe to smother a point-blank chance by Toby Petersen. Robidas did tie the game with 5:36 showing, as he moved up center ice and unloaded a blast off the left post from 35 feet out.
A delay-of-game penalty to Flyers defenseman Kimmo Timonen for shooting the puck over the glass with 1:37 remaining created a 4-on-3 for the Stars, but expert penalty killing kept Dallas off the board for the rest of regulation and a sliver of overtime.
Bobrovsky then did the splits on a rolling blast earmarked for the far left portion of the net from Goligoski less than a minute into OT.
Philadelphia improved to 3-4 in shootouts this season, and Dallas fell to 5-6…It was the first-ever shootout between these clubs…The Flyers won for just the third time in Dallas since the Stars moved from Minnesota to Texas, upping their mark to 3-5-3 in 11 games…Richards hit the 20-goal plateau for the fourth straight season…Meszaros and Matt Carle notched two assists for the victors…The only year the Flyers haven’t made the playoffs since the lockout-shortened 1995 campaign was in 2006-07.