Elliot also added a helper to cap off a three-point effort and Evan Brophey netted the third Lake Erie goal. Netminder Gerald Coleman was strong in what was his 11th straight start, as he turned away 29 of 30 Rochester shots while also picking up an assist.
Phil Varone tallied the lone goal for Rochester in the contest, with assists going to Travis Turnbull and goaltender David Leggio. Leggio also finished the night with 31 saves between the pipes.
The Monsters got on the board first at the 12:18 mark of the opening period, as Elliot scored his fourth of the season. The 21-year-old blueliner fired a shot from center point that found its way through a screen and snuck past Leggio.
Elliot buried his second goal of the frame less than two minutes later to double the Lake Erie lead to 2-0, depositing a wrister from the high-slot to the top corner of the net.
The Monsters opened up a 3-0 advantage with a power-play tally at 8:56 of the middle period, as Brophey jammed home a loose puck at the mouth of the Rochester crease for his 14th of the season.
Varone converted on a shorthanded breakaway at 11:25 of the third period to cut the Rochester deficit to 3-1. Turnbull and Leggio assisted on Varone's eighth of the season as the rookie forward took over the team lead in points.
Having already met eight times this season, the Amerks return home to The Blue Cross Arena on Sunday, February 19 to renew their heated divisional rivalry with the Hamilton Bulldogs as both teams play their third game in as many nights. The puck drops at 5:05 p.m.