Umberger, a Pittsburgh native, beat Marc-Andre Fleury 6:50 into the third to break a tie and Read followed with a backhander to help the Flyers improve to 12-2-1 at Consol Energy Center since the arena opened in 2010.
"Coming in here tonight and beating a good team on their ice to finish off a road trip, to me that shows a lot of character," Umberger said.
Though the game featured two U.S. teams, the sell-out crowd sang "O Canada" before the opening faceoff to honor a Canadian soldier killed in attack in Ottawa on Wednesday.
"I thought it was a special tribute tonight," said Penguins coach Mike Johnston, who was born in Nova Scotia and has coached throughout Canada. "Certainly when those events happen, they strike everybody."
Sean Couturier had a goal and an assist, Mark Streit and Pierre-Edouard Bellemare also scored for the Flyers. Ray Emery stopped 21 shots as Philadelphia rebounded from a 4-0 loss in Chicago on Tuesday night to outplay the well-rested Penguins, playing for the first time in four days.
"I think we could definitely be sharper," Penguins center Sidney Crosby said. "Whether that's because we haven't played a lot of games or we weren't focused on executing the right way, It could be either of the two but we definitely weren't sharp in a lot of areas."
Nick Spaling had a goal and an assist for Pittsburgh. Pascal Dupuis and Marcel Goc also scored for Pittsburgh, but the Penguins were plagued by defensive breakdowns. Marc-Andre Fleury made 28 saves but was consistently put in tough spots as Philadelphia expertly counter-attacked to catch the Penguins out of position.
"I think it was one of those games where their energy caught fire and ours took a step back," Johnston said.
Umberger, who grew up 20 minutes east of the arena, scored his first goal of the season when he blasted a feed from Claude Giroux by Fleury to break a 2-2 tie. Read's first tally was considerably easier, tucking a backhander past the sprawled Fleury to give the Flyers a cushion.
Goc drew Pittsburgh within a goal when he beat Emery with 2:57 remaining, but Couturier flipped a puck the length of the ice into an empty net with 26 seconds left as the Flyers finished up a 2-1 road trip.
"I like the way we checked," Flyers coach Craig Berube said. "I think in the neutral zone we did a real good job without the puck and took away their speed for the most part."
The Penguins unveiled a new third jersey that replicated the uniform worn by the Mario Lemieux-led teams that won consecutive Stanley Cups in 1991 and 1992. The new old duds seemed to give Pittsburgh early energy.
Spaling gave the Penguins an early lead with his first goal since being acquired in a draft day trade from Nashville in June, jumping on a rebound and beating Emery over his right shoulder just 3:50 into the game. The score seemed to temporarily deflate the Flyers. Pittsburgh controlled play for an extended stretch at one point, keeping the puck in the Philadelphia zone for the better part of a minute at even strength. The effort drew a standing ovation but no results, as Emery kept Philadelphia in it.
The Flyers quickly gathered themselves and eventually countered. Streit's slap shot from the point appeared to be deflected by Pittsburgh's Evgeni Malkin to tie it and Bellemare, a 29-year-old rookie from France, scored his first NHL goal with a delicate tip-in off a centering pass from Couturier.
Dupuis evened it 9 minutes into the second when Paul Martin's shot from the point hit him and found its way around Emery but the Flyers controlled the third period to win going away.
Pittsburgh's top-ranked power play went 0 for 2, the first time this season the Penguins have not scored with the man advantage. ... Flyers C Zac Rinaldo left with an upper- body injury at the end of the first period and did not return. ... The Penguins play in Detroit on Thursday night. ... The Flyers host Detroit on Saturday night.