Matt Martin tied the game 23 seconds into the third period for New York (31-15-6), which extended its point streak to five games (3-0-2) and moved back into third place in the Metropolitan Division, one point ahead of the Columbus Blue Jackets. Thomas Greiss made 22 saves.
"Anytime you score and help the team win, just do anything you can to help the team win and get two points, especially this time of year going into the playoff run here, it's huge," Bellows said.
WATCH: [All Kings vs. Islanders highlights]
Ben Hutton had a goal and an assist for Los Angeles (19-31-5), which has lost three in a row and is 1-7-1 in its past nine games. Jonathan Quick made 28 saves.
"We've played close games, tight games where I thought we deserved better. Tonight wasn't one of those," Kings coach Todd McLellan said. "They were the better team. We probably got what we deserved.
"I did not like our play in our end or around our blue paint one bit. We weren't in shooting lanes, as they were. We got what we deserved. We've got to be better than we were tonight."
Bellows scored his first NHL goal at 10:22 of the second when he took a pass from Anthony Beauvillier and put a wrist shot past Quick to make it 3-2.
"Pretty special moment," Bellows said. "I was pretty speechless at the time, I didn't really know what to do. Once I got back to the bench, I knew I had to move on and focus on the next shift."