Thursday's game in Philadelphia, however, will be their last meeting this season.
The Flyers (14-7-6) have faced the Hurricanes (13-12-3) three times since Nov. 26 and won twice. Their only loss came Nov. 28 at the Wachovia Center - 3-2 in overtime.
That defeat was one of the Flyers' few of late. In its last 14 games, Philadelphia has gone 10-1-3, including two wins at Carolina - 3-1 on Nov. 26 and 2-1 in overtime Saturday.
"We keep trying to help ourselves as best we can," Flyers coach John Stevens said. "We have to tackle each game as it comes."
The Flyers have scored four goals in six of their last 13 games, and helping Philadelphia become one of the league's most potent offenses - 3.26 goals per game - is Jeff Carter.
Among the league leaders with 20 goals, Carter has scored four times in the last four games, including once in Tuesday's 4-3 win over the New York Islanders. The former first-round pick had a career-high 29 goals last season.
With two assists Tuesday, Mike Richards extended his point streak to five games. He has five goals and three assists over that span.
Carter has two goals and two assists this season against the Hurricanes, while Richards has scored once. Simon Gagne, the team's leader with 33 points, has four points in the three meetings.
Martin Biron yielded at least three goals in his seventh straight start Tuesday, but improved to 4-1-2 in that span. The Flyers, however, could look to backup Antero Niittymaki Thursday after he won both meetings this season against the Hurricanes, giving up one goal in each.
Leighton lost 5-2 to Pittsburgh on Dec. 4 and also took the loss Saturday against the Flyers, but earned a 3-1 victory Sunday over Washington.
Among his season-high 38 saves was a stop on Alex Ovechkin's penalty shot with 1.2 seconds left in the second period.
"He was going to have to be the difference in the game," said Carolina coach Paul Maurice, who earned his first win since taking over for the fired Peter Laviolette. "The upside would be that if he could do that for us, we would look at it as three out of four points and that he was a big, big part of it."
Leighton has lost twice in his career to Philadelphia, giving up two goals in each game.
The victory over the Capitals broke the Hurricanes' three-game losing streak and was just their second in the last eight. A lackluster offense can take some of the blame as Carolina has scored two goals or fewer six times in that stretch.
Ray Whitney, who scored twice Sunday and has a team-leading 21 points, has four points in the last three games. However, he has one assist in the three games against Philadelphia.
Of the five goals the Hurricanes have scored against the Flyers this season, Sergei Samsonov has two, including one in overtime on Nov. 28.
Philadelphia has gone 7-0-3 in the last 10 meetings with Carolina, but dropped the last two at the Wachovia Center.