Shane Prince, Thomas Hickey and Cal Clutterbuck also scored, helping the Islanders to the victory in both teams' first game after their respective five-day byes.
The Islanders are unbeaten in this season's "Battle of New York" after edging the Rangers 4-3 in their first meeting October 19, with Isles leading scorer John Tavares netting the decisive goal in the shootout.
With his record-setting outing, Barzal pushed his point total for the season up to 44 (15 goals, 29 assists) in 44 games, passing Vancouver's Brock Boeser for the rookie scoring lead.
The Rangers (22-16-5) had been hoping to rectify their slow starts, but they were quickly behind and then gave up three goals in the first seven minutes of the second period to go down, 5-1.
The Rangers have lost two in a row and three of their last four. At this point, Ondrej Pavelec took a place on the bench, and Henrik Lundqvist came in.
"I think the Rangers are starting to look and say, 'are there other moves we can make?' Similar to the one with Derek Stepan in Arizona at last year's draft", Sportsnet's Elliotte Friedman said on Saturday. "You just have to go to yourself right now, try to play your best game to try to help the group, and not figure out everything".
After failing to get anything at all going, the second period came to a close with the Rangers down by four.
It was practically all Islanders after that, as they rattled off four straight goals.
Mathew Barzal had two goals and three assists, Anthony Beauvillier added two goals and an assist, and the New York Islanders beat the New York Rangers 7-2 on Saturday for their ninth win in the past 10 meetings of the crosstown rivals.
Danault hit in head by Chara's slap shot; Bruins top Habs MONTREAL - Canadiens center Phillip Danault was awake and moving after taking Zdeno Chara's slap shot to the head. Barzal scored back-to-back goals in the second (at 0:37 and 4:11), and Beauvillier added his second at 6:51 of the middle period. Claude Giroux had the primary assist on two power-play goals and Brian Elliott made 26 saves as Philadelphia won in New Jersey for the first time since February 16, 2016.
The Flyers, who took the first five penalties, killed off 5 of 7 and scored on their only two extra-man chances, with Couturier's second on a Giroux setup giving Philadelphia a 3-2 lead with 1:44 left in the second period. NY has dropped five of their last six at MSG against the Islanders and when these two sides meet up the goal judges have been getting some serious work as the over is 5-1-1 in their last seven meetings and is over in the Islanders' last 27 or 37 tries which gives us a lean here that this one is going to hit the over as both teams have a boat load of talent in the offensive zone.
No. 4 Spartans still in a funk after loss to MI
These two teams aren't scheduled to play again this season. "We're the ones that are supposed to be out-toughing people". And there was nothing they could do about it. "Their offense didn't beat us", he said. "It's never a good feeling".