Brassard had the primary assists on Mark Stone's goal in the first period and Thomas Chabot's tally in the third. The former Ranger center tallied for the fourth straight game late in the second period.
Matt Duchene and Chabot collected a goal and assist as Ottawa won its fifth straight home game and for the sixth time in the last nine games overall.
Johnny Oduya and Magnus Paajarvi also scored, and Craig Anderson made 35 saves for Ottawa.
Michael Grabner scored twice, and former Senator Mika Zibanejad netted a power-play goal for the Rangers, who lost for the 10th time in 13 games.
Henrik Lundqvist allowed five goals for the third time this season and was pulled after allowing Chabot's goal.
Ottawa took a lead 63 seconds into the contest.
Smith whipped a pass from the corner to Brassard, who was unguarded behind the net. Brassard patiently waited for Stone to reach the high slot and he one-timed the pass past Lundqvist for his 19th goal of the season.
The Senators made it 2-0 when Erik Karlsson faked a shot from the middle of the ice to freeze the Rangers but instead whipped the pass to Oduya, who lifted a shot from about 35 feet out by Lundqvist.
Grabner jammed in a rebound past Anderson for his late in the first but Ottawa regained a two-goal lead with 8:01 left in the second when Duchene re-directed Cody Ceci's rising shot over Lundqvist's left pad.
With 5:29 remaining, the Rangers made it a one-goal game for the second time when Zibanejad sped past Tom Pyatt and defenseman Ben Harpur after controlling a long pass from Mats Zuccarello.
Zibanejad made a move to get Anderson out of position and lifted a shot over the stick.
Ottawa took its third two-goal lead when Brassard re-directed Mark Borowiecki's pass into the vacated left side of the net with 67 seconds left in the second period.
The Senators scored their fifth goal when Chabot's wraparound attempt went off New York defenseman Nick Holden's left skate into the vacated net. With about five minutes remaining, Grabner made a spin move and one-timed Kevin Hayes' pass but Paajarvi scored a little over two minutes later.
--Field Level Media
NY Rangers | Ottawa | |
Michael Grabner 2 | Points | Derick Brassard 3 |
Michael Grabner 2 | Goals | Derick Brassard 1 |
Pavel Buchnevich 1 | Assists | Derick Brassard 2 |
Mika Zibanejad 1 | Power Play Goals | N/A |
N/A | Short Handed Goals | N/A |
Brandon Halverson .833 | Save Percentage | Craig Anderson .921 |
Henrik Lundqvist 22 | Saves | Craig Anderson 35 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
NY Rangers | 38 | 3 | 1-2 | 2-2 | 4 | 33 |
Ottawa | 33 | 6 | 0-2 | 1-2 | 4 | 24 |