NEW YORK — The Rangers have been playing better since the holiday break, but for that to matter, it has to translate into results. It did Thursday night against the New Jersey Devils, a rival team near the top of the standings that blew out New York the last time they met.

In desperate need of wins, the Rangers notched an overtime victory over the Devils thanks to a goal from Sam Carrick.

In what’s been a rough season at Madison Square Garden, few Rangers losses hurt more than the two lopsided defeats at the hands of the Devils earlier in the year. So perhaps there was some extra meaning to Thursday night’s thrilling 3-2 overtime win over their cross-river rivals,