Sidney Crosby and Josh Archibald also scored in Pittsburgh's fifth consecutive victory. Teddy Blueger had three assists, and Tristan Jarry made 29 saves.
''I just think we're playing a more complete game,'' Penguins coach Mike Sullivan said. ''I feel like we're playing a more conscientious game. I just give the players a lot of credit. They're paying attention to details out there. They're making good decisions. They're competing hard. It's a collective effort out there from everybody on the ice.''
Crosby's team-leading 11th goal in the first period was also his 52nd in 81 games against Philadelphia, breaking Hall of Famer Mario Lemieux's record for most goals against the Flyers.
Philadelphia visits the New York Islanders on Saturday night. It is hoping to avoid its third double-digit losing streak in less than 12 months.
The Flyers became the first team in NHL history to have a pair of 10-game losing streaks within the first 40 games of the season last year: They dropped 10 in a row from Nov. 18 to Dec. 8 before setting a franchise record with 13 straight defeats between Dec. 30 and Jan. 25.
The first skid cost coach Alain Vigneault his job, and the second one was overseen by interim coach Mike Yeo.
After a surprisingly good start under John Tortorella this season, when Philadelphia won five of seven, the rebuilding Flyers haven't been able to keep up the momentum.
''We were flat,'' Tortorella said. ''I don't think the guys are spending too much time with what the record is or how many we've lost. They're trying to be better each and every night. I just don't think we had much juice tonight.''
Kevin Hayes scored for Philadelphia.
Crosby scored with 30.5 seconds left in the first. Marcus Pettersson took a slap shot from long range, and Crosby nimbly deflected it from the slot high over goalie Carter Hart.
Crosby now has 121 points against the Flyers, with only Lemieux's 124 ahead of him on the points list against Philadelphia.
Other than Crosby's goal, all of Pittsburgh's scoring came from its fourth line, with Poehling and Archibald centered by Blueger.
''Obviously we're here for a reason, that's to do well defensively,'' Poehling said. ''But we all want to produce offensively as well. And I think that's part of our game that we all pride ourselves on. We've been playing really well defensively and then offensively, I think we've gotten a lot of chances in the past few games. It's been a lot of fun.''
Hart made several strong stops early, including glove saves on Jeff Carter and Bryan Rust, before the Penguins broke through after a costly turnover by Philadelphia defenseman Justin Braun following a faceoff outside of the Flyers zone.
Blueger pounced on the puck after Braun fanned on a passing attempt. Hart stopped Blueger's shot, but the rebound fell right to the stick of Archibald, who backhanded it home for his fourth goal of the season with 8:23 left in the first.
Poehling's two second-period goals put the Penguins up 4-0. He scored on a great deflection from the slot, similar to Crosby's, 2:59 into the period. With 6:23 left, he sent the puck toward the crease from behind the net and it deflected off Hart's stick and over the goal line.
''It's huge,'' Blueger said of his line's contribution. ''I think it always kind of boosts the morale. As much as we've got to be responsible defensively and defend well, and (play on the penalty kill) and all those things, I think at the end of the day scoring goals is the best feeling in the world.''
Tortorella lifted Hart for Felix Sandstrom after that goal.
''Wasn't Carter,'' Tortorella said. ''Nothing to do with Carter.''
Philadelphia's Nick Deslauriers won a one-sided fight with Pettersson early in the second period, landing several hard rights to Pettersson's jaw and head. The Penguins defenseman was standing up for partner Kris Letang after Deslauriers leveled Letang into the boards behind the net.
Later in the period, Philadelphia's Nick Seeler sparred with Brock McGinn, with Seeler landing a heavy right early en route to a victory.
Flyers: F Travis Konecny (upper body) missed his fourth contest in a row, and F Scott Laughton (upper body) was sidelined for the third consecutive game. Both are expected to be sidelined for two weeks.
Penguins: Host Toronto on Saturday night.
Flyers: At Washington on Wednesday night.
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