Sidney Crosby tied things late in regulation with a 5-on-3 power-play goal and Kennedy won it with his fifth goal of the season, a wrist shot from the left circle.
"I think we're a pretty confident team right now," Kennedy said. "I think we know if we stay on the plan and do all the little things we can be successful."
Marc-Andre Fleury stopped 27 shots for Pittsburgh, which remained unbeaten in March. The Penguins played without injured defenseman Kris Letang and reigning league MVP Evgeni Malkin, who remains sidelined with an upper body injury.
Malkin could be back by the end of the week and he'll find a new face on the second line he shares with James Neal. Pittsburgh traded away promising defenseman prospect Joe Morrow early Sunday evening for Dallas Stars captain Brenden Morrow, hoping the veteran forward will give the Penguins some added punch in the playoffs.
"I think we all pride ourselves in playing a certain way and I think he fits right into that mold," said Crosby, who played with Morrow for Team Canada in the 2010 Winter Olympics. "I think he's going to add to those things and add to what we have here. It's a great acquisition and we're pretty excited."
The late flurry ruined a brilliant night by Philadelphia's Ilya Bryzgalov, who stopped 33 shots but had no answer when Kennedy's sizzling wrister sailed under the crossbar and sent his teammates spilling onto the ice.
"I thought we came in here and played a good road game," Philadelphia coach Peter Laviolette said. "It's unfortunate."
Claude Giroux scored his 10th goal of the season late in the second period for Philadelphia, but the Flyers couldn't make it hold up on a night they played without forward Danny Briere and defenseman Nicklas Grossman. Briere sustained an upper body injury in practice on Saturday and is day to day.
At the moment, so are Philadelphia's postseason chances. The Flyers are 13th in the crowded Eastern Conference, though they hope to build on the nearly flawless hockey they played for the game's first 50 minutes.
"We've got to take positives from this," Giroux said. "We got a point, but we need another point."
Philadelphia was in control until Wayne Simmonds and Kimmo Timonen went off with penalties 23 seconds apart with less than 8 minutes remaining. Crosby, the NHL's leading scorer, took advantage of the ensuing 5-on-3 by wristing a shot by Bryzgalov with 6:14 remaining in regulation.
Both teams exchanged opportunities in the final minutes before heading to the extra period when Kennedy found a way to keep Pittsburgh perfect in overtime. The Penguins are now 4-0 when the game is tied at the end of regulation.
The two rivals have played some of hockey's most entertaining games over the last few years, including a remarkable playoff series last year in which they combined for 56 goals in six entertaining games.
Their first three matchups this season were more of the same. The last meeting earlier this month featured the Penguins rallying from three goals down to win 5-4 and push the winning streak to a modest three games.
This time things were a bit more understated.
Giroux finally broke through on the power play late in the second period thanks to a fortunate bounce. He skated into Pittsburgh's zone and attempted to slip a cross-ice pass to a teammate. The puck bounced off the stick of Pittsburgh's Pascal Dupuis and right back to Giroux, who fired it by Fleury to put the Flyers in front.
It didn't last, as the Penguins picked up their eighth one-goal victory during the streak, which is now the 11th streak of at least 12 games in NHL history.
It also served as a bounce-back game of sorts for the Penguins, who were outplayed for long stretches of a 4-2 win over the New York Islanders on Friday. They were more disciplined on Sunday, taking just one penalty, and continued to play responsible defensively. Pittsburgh has allowed just nine goals over its last eight games.
"We had played a couple games that weren't our best hockey and had periods where it wasn't even close to the way we needed to play," Crosby said. "Tonight we were much better and I think we got rewarded at the end for it."
The Penguins are 4-6 this season when trailing after two periods. ... The crowd of 18,662 set a record at Consol Energy Center. ... Pittsburgh hosts Montreal on Tuesday night. ... The Flyers begin a five-game homestand on Tuesday against the New York Rangers.
Copyright by STATS LLC and The Associated Press
PITTSBURGH, PA - MARCH 24: Paul Martin #7 of the Pittsburgh Penguins moves the puck in front of the defense of...