Beauvillier ran his season tally up to seven goals, while Barzal now leads all NHL rookies with 15. Barzal also had three assists in the contest.
Shane Prince, Thomas Hickey and Cal Clutterbuck also scored a goal apiece for the Islanders, who won their second straight game following a season-high five-game losing streak. Jordan Eberle led the team with four assists in the blowout.
Kevin Hayes and Mika Zibanejad scored the only goals for the Rangers, who entered the game with a one-point lead for the top wild-card spot in the Eastern Conference.
The Rangers have lost two in a row and three of their last four.
The Islanders are unbeaten in this season's "Battle of New York" after edging the Rangers 4-3 in their first meeting Oct. 19, with Isles leading scorer John Tavares netting the decisive goal in the shootout.
Islanders goalie Jaroslav Halak kept the Rangers at bay with a 37-save performance.
Two goalies saw action for the Rangers, with Henrik Lundqvist relieving backup Ondrej Pavelec after Pavelec allowed five goals on 19 shots. Lundqvist finished with 16 saves on 18 shots.
Both teams were coming off their five-day bye weeks, but it was the Rangers who showed the most rust.
Beauvillier opened the scoring for the Isles just 6:06 into the opening period, but Hayes tied the game with his 10th goal of the campaign at 14:25 on a power-play strike.
It was practically all Islanders after that, as they rattled off four straight goals.
Prince scored his first goal of the season at 16:25 of the first, putting the Isles ahead for good. 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.
Zibanejad's 14th goal of the campaign made it a 5-2 game at 9:05 of the third, but goals from Hickey, his second of the season, and Clutterbuck, his eighth, buried any hopes of a Rangers' comeback.
The Rangers travel to Pittsburgh on Sunday, while the Islanders visit Montreal on Monday.
--Field Level Media
NY Islanders | NY Rangers | |
Mathew Barzal 5 | Points | Kevin Hayes 1 |
Mathew Barzal 2 | Goals | Kevin Hayes 1 |
Jordan Eberle 4 | Assists | Ryan McDonagh 1 |
N/A | Power Play Goals | Kevin Hayes 1 |
N/A | Short Handed Goals | N/A |
Jaroslav Halak .949 | Save Percentage | Henrik Lundqvist .889 |
Jaroslav Halak 37 | Saves | Henrik Lundqvist 16 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
NY Islanders | 37 | 7 | 0-2 | 2-3 | 6 | 30 |
NY Rangers | 39 | 2 | 1-3 | 2-2 | 4 | 34 |