The Flyers, who got a solid effort from goalie Ilya Bryzgalov, wrapped up the fifth seed and will face the Pens in the first round.
Read leads NHL rookies in goals (24), game-winning goals (6) and shooting percentage.
Trailing 1-0, the Flyers scored the equalizer on defenseman Marc-Andre Bourdon's blast from the right point with 13:55 left in the third period. Claude Giroux picked up an assist, giving him 93 points - equaling the most by a Flyer since Eric Lindros had 93 in 1998-99.
With 11:13 to go, Bryzgalov robbed Tyler Ennis out front to keep the game tied.
Former Flyer Ville Leino out-battled defenseman Matt Carle and scored on a rebound with 2:34 left in the second period to snap a scoreless tie.
With Bryzgalov scrambling out of the net, Drew Stafford's backhander from in tight went off the right post, but the much-maligned Leino got position on Carle and rammed in the rebound for just his eighth goal of the season.
In July, Leino signed a six-year, $27 million free-agent deal with the Sabres.
Opponents have scored first in 23 of the Flyers' last 31 games, including nine of the last 11 contests.
Shortly after Leino's goal, the Flyers went on a two-on-one, but Sean Couturier, trying to convert Jakub Voracek's feed, rattled a shot off the left post.
Earlier, Jody Shelley knocked his own rebound past Buffalo goalie Ryan Miller from an odd angle, but as the puck was about to trickle into the net, defenseman Andrej Sekera swept it out of harm's way with 16:30 left in the second period.
A little less than two minutes later, Miller made a nice stop on Jaromir Jagr's drive from the right circle.
In a sleepy first period in which the Flyers held a 9-3 shots edge, the best scoring chance came while the home team was shorthanded and Matt read went in on a breakaway. But goalie Ryan Miller poke checked the puck away at the last second, keeping the game scoreless.
It marked the 50th time in the last 54 games that the Flyers have not had a lead at any point during the first 10 minutes.
Bryzgalov was making his second straight start after missing three games with a chip fracture in his right foot. He made 25 saves.
The Flyers finished with a 22-13-6 home record.
Contact staff writer Sam Carchidi at firstname.lastname@example.org, or on Twitter @BroadStBull.