Simon Gagne scored for the Flyers, who had dropped six in a row five times in their 40-year history -- including twice this season. The Flyers have the fewest points in the NHL (20) and have only three victories at home, also a league low.
Cam Ward stopped 29 shots as the Hurricanes won their second consecutive game after snapping their season-high five-game losing streak with a 3-2 win at Tampa Bay last Saturday.
"We've been struggling, too," Ward said. "We knew that we couldn't take them lightly. It was important that we were mentally ready because they still have a very good first line and some young guys working hard."
Ward's best save came late in the second period when a point-blank shot by Jeff Carter bounced off his shoulder.
Philadelphia coach John Stevens said the Flyers must find a way to compete for 60 minutes in order to start winning again.
"In the second period we killed way too many penalties, we flat out just didn't compete," Stevens explained. "You can't win in this league when you don't compete. We didn't win any board battles. We didn't finish any checks.
"We just let them do whatever they want, and that is just absolutely unacceptable."
Philadelphia goalie Antero Niittymaki stopped 40 of a season-high 42 shots allowed by the Flyers, who were outshot 17-5 in the second period.
Williams put the Hurricanes ahead at 12:41 of the first when he redirected Andrew Hutchinson's slap shot from the point over Niittymaki's glove for his 15th goal of the season.
"We were scrambling, working it around," Williams said. "I happened to be there and it tipped the toe of my stick."
Babchuk made it 2-0 with his second goal, a slap shot from the left circle at 2:42 of the second period.
"We had lots of opportunities," Carolina coach Peter Laviolette said. "It's 2-0 after two and you're nervous that it could get close because it could have been more than that. I thought our guys played pedal to the metal offensively and they got the looks they wanted and either hit the post or missed the net, or Niittymaki made big saves."
Gagne got the Flyers within one at 14:05 of the third when he deflected Randy Jones' slap shot from the right circle high over Ward's shoulder.
Philadelphia center Peter Forsberg missed his 10th game, this time because of a concussion sustained during a 4-1 loss at Washington last Saturday. The Flyers are 0-7-3 when Forsberg is out of the lineup.
"When times are tough you cannot get down," Philadelphia's Todd Fedoruk said. "You do not give up in situations like this. We have to play desperate hockey."
Carter returned to the lineup after missing 20 games with a broken left ankle. ... Flyers D Jussi Timonen was sidelined with the flu. ... Carolina C Rod Brind'Amour returned after missing four games with a lower body injury. ... Hurricanes C Kevyn Adams was scratched after undergoing wrist surgery earlier on Tuesday. ... Williams extended his season-high point streak to five games (four goals, two assists). ... Carolina's Eric Staal hit the left post early in the second period and Cory Stillman did the same with a shot at an open net in the closing seconds.