Eller -- who had scored four times in his first 36 games this season -- matched that total while leading the Canadiens to their largest goal output of the campaign. Montreal had won only once in its previous eight games and scored six times in that victory, Dec. 27 over Ottawa.
Eller put Montreal in front for good at 2-1 with 5:53 left in the opening period and then scored three times in the span of 8:19 of the third. The last of the goals came on a penalty shot.
Carey Price made 24 saves in the victory.
Winnipeg had a three-game winning streak snapped.