"Getting back-to-back]*
Nico Hischier and Kyle Palmieri scored for the Devils (39-28-8), who are two points behind the Philadelphia Flyers for the first wild card into the Stanley Cup Playoffs from the East. The Devils have defeated the Lightning and Penguins three times each this season.
Ondrej Palat scored and Andrei Vasilevskiy made 29 saves for the Lightning (51-20-4), who are first in the Atlantic Division, four points ahead of the Boston Bruins, who have two games in hand.
"They are desperate and those are dangerous teams," Tampa Bay forward Chris Kunitz said. "We have to match that urgency. We have to be a better team and go out and be better than them on every single shift, and I feel they did a better job of doing that."
Kinkaid made 11 saves in the third period to prevent the Lightning from taking the NHL points lead. Tampa Bay and the Nashville Predators each have 106 points.
"Keith has been a difference-maker," Devils coach John Hynes said. "He has really come in and played well, has made key saves at key times. He obviously won quite a few games and been a real important factor for us in remaining competitive in the playoff race.
"We would like to see him continue that at that level as well."