Sidney Crosby tied things late in regulation and Kennedy won it with his fifth goal of the season, a wrist shot from the left circle.
Marc-Andre Fleury stopped 27 shots for Pittsburgh, which remained unbeaten in March.
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.
Ilya Bryzgalov made 33 saves but let two slip by late.
The Penguins played without injured defenseman Kris Letang and reigning NHL Evgeni Malkin, who remains sidelined with an upper body injury.
The Eastern Conference's top team keeps on rolling, however, and help is on the way. Pittsburgh traded away promising defenseman prospect Joe Morrow early Sunday evening for Dallas Stars captain Brenden Morrow.
The Penguins hope Morrow's physical play will help them in the playoffs. Kennedy provided the punch this time as Pittsburgh sent the sinking Flyers packing with another late rally.
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 sizzled a wrist shot that clanged off the back of the net and sent his teammates spilling onto the ice.
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.
