Kulikov's shot from the right circle beat Martin Brodeur on the far side and was his first goal of the season.
The Panthers have won two in a row at home for the first time this season.
Steve Bernier scored two goals for the Devils and Brodeur stopped 27 shots. The Devils have lost three straight.
Matthias' second goal tied the game at 2 with 27 seconds left in regulation. He grabbed a rebound in front of the crease and wristed it past Brodeur.
Matthias has a career-high 14 goals and 11 in the past 16 games. Matthias also had two goals in Thursday's 5-4 shootout win over Buffalo.
Tied at 1, Bernier scored his second goal at 7:57 of the third on a power play. Henrik Tallinder took a shot from the high slot and Bernier deflected it into the net to give the Devils a 2-1 lead.
Bernier hadn't scored a goal since March 2 at Buffalo and this was his first multi-goal game since Feb. 3 at the New York Islanders.
The Devils took a 1-0 lead on Bernier's first goal. The Panthers turned the puck over on a pass from behind the net and Bernier backhanded in a pass from Ryan Carter at 3:42 of the first.
The Panthers tied it at 1 on a power-play goal by Matthias. Jonathan Huberdeau took a shot from the right circle and Matthias deflected it in at 12:55.
Notes: Panthers RW George Parros returned from an upper-body injury. ... Panthers F Greg Rallo was reassigned to AHL San Antonio. ... The previous time the Devils visited the Panthers they eliminated them from the opening round of the playoffs with a 3-2 double-overtime win in Game 7.