Kuba fired a slap shot from the left point past goalie Ilya Bryzgalov, and Nick Foligno sealed the win with an empty-net goal with 45 seconds to go.
Colin Greening and Erik Karlsson scored earlier in the third period for the Senators, who erased a 4-2 deficit. Daniel Alfredsson and Chris Neil had goals in the first, and Craig Anderson made 33 saves for Ottawa, which is on a 5-0-1 run - including a 3-2 overtime loss at Philadelphia on Saturday.
Matt Read scored a power-play goal in the second and assisted on one of three Flyers goals in the first.
Andrei Meszaros scored 2:32 into his 500th NHL game to draw Philadelphia even at 1. Marc-Andre Bourdon and Sean Couturier had goals 28 seconds apart to give the Flyers a 3-2 lead later in the first period.
Read's goal 14:08 into the second - the third of the game by a Philadelphia rookie - was his 13th of the season. Read gave the Flyers a 4-2 lead and tied Edmonton's Ryan Nugent-Hopkins for the most goals by an NHL rookie this season.
Bryzgalov stopped 32 shots for Philadelphia, which had won two in a row and three of four.
Greening got credit for his ninth goal 3:11 into the third to bring the Senators within 4-3. Philadelphia defenseman Matt Carle redirected Greening's centering pass beyond Bryzgalov for the goal.
Karlsson tied it at 4 with an unassisted effort. The high-scoring defenseman took the puck away from Jaromir Jagr and drove in to beat Bryzgalov for his sixth goal.
Jagr returned to the Flyers' lineup after missing two games because of a groin injury sustained in the Winter Classic. He was limited to 7:09 of ice time in Philadelphia's 3-2 loss to the New York Rangers on Monday.
Alfredsson scored the first of five goals in the first period 54 seconds in. Kyle Turris fed a pass to the slot to the Ottawa captain, who netted his fourth goal in six games.
Meszaros, who began his career with Ottawa, one-timed Max Talbot's pass and drove a shot from the right point through traffic past Anderson.
A scramble in the Flyers' goal mouth resulted in the Senators taking a 2-1 lead at 8:25. After initially signaling no goal on the ice, referee Brad Watson pointed to center ice to the delight of the sold-out crowd after a long video review determined that the puck crossed the goal line on Neil's shot into Bryzgalov's glove.
NOTES: J.P. Arencibia, Brett Lawrie, Ricky Romero and Casey Janssen of the Toronto Blue Jays were in attendance. ... Ottawa will begin a three-game trip at Pittsburgh on Tuesday. ... The Senators, who host the NHL All-Star game later this month, will play nine of their next 10 games on the road. ... It was Ottawa's 14th sellout in 23 home games. ... The Flyers are 5-2 in the first game of back-to-backs this season and 3-2-1 in the second.