Nick Foligno scored the other goal for the Senators, and Ryan Shannon added two assists. Craig Anderson made 30 saves for his third win in four starts since the Senators (21-32-9) acquired him from the Colorado Avalanche last week.
Scott Hartnell had the only goal for Eastern Conference-leading Philadelphia (40-16-6), which got 26 saves from Brian Boucher but lost for the second time in three games.
Phillips scored his first of the season to give Ottawa a 3-1 lead at 11:15 of the third. The veteran defenseman has been the subject of trade rumors and could be dealt before the NHL trade deadline on Monday.
Following a first period in which the Senators trailed 1-0 and were thoroughly dominated by the Flyers, Ottawa turned the tables over the final 40 minutes and outshot Philadelphia 27-15 the rest of the way.
Foligno outworked two Flyers in the corner on a power play before putting a shot over Boucher's shoulder at 12:18 of the second.
Condra scored his first goal at 16:10 on a great feed from Shannon off a cycle behind the Philadelphia net.
Phillips scored on a shot from the point at 11:15 of the third to provide some insurance, and Condra made it 4-1 with a deflection on the power play at 18:35.
Hartnell gave the Flyers a 1-0 lead with 20 seconds remaining in the first period.
Notes: Senators captain Daniel Alfredsson missed his eighth straight game because of a sore back. Defenseman Sergei Gonchar missed his fourth game due to a lower body injury. ... Jason Spezza ranks second in Senators scoring with 507 points. ... Hartnell is two points shy of 400 in the NHL.