Rolston and Kovalchuk each had a goal and an assist in regulation and added shootout goals, with Rolston netting the winner in the sixth round in the Devils' 3-2 victory over the New York Islanders on Sunday.
"I find the shootouts to be tougher because there's more pressure on you," Rolston said.
The Devils are 20-2-2 in their last 24 games to improve to 30-31-4. They are eight points behind eighth-place Buffalo in the race for the final Eastern Conference playoff spot.
Kovalchuk broke a 1-1 tie with a goal at 2:52 of the final period when he moved in and beat Al Montoya over his glove with a high wrist shot.
"We got a lot of chances today," Kovalchuk said. "I just go out there and try to do my best."
Brodeur stopped 20 shots.
Josh Bailey also scored for the Islanders, and Montoya made 27 saves.
"There are times where you're going to get frustrated," Islanders center Frans Neilsen said. "You have to hold your head high and not get frustrated."
New Jersey opened the scoring at 4:09 of the second period, and just 9 seconds into their first power play. Kovalchuk fed the puck to Rolston at the point, and he let loose a slap shot that beat a screened Montoya.
Rolston praised Montoya.
"He's played very well for them," Rolston said. "We knew that coming in, and we were trying to figure out how to beat him."
The Islanders tied it with less than 3 minutes left in the period on their second power play. Bailey, standing in the right circle, took a shot that Brodeur stopped, but the rebound left a trail of bodies scrambling. Bailey moved in and found an open net to put it home.