The Canadiens had an 11-game point streak halted Tuesday against the New York Islanders, but quickly took charge against the Hurricanes on first-period goals from Brandon Prust and Josh Gorges.
Carolina came back to tie it in the second with Jordan Staal and Drayson Bowman producing the goals.
Eller then tipped in a shot by Gorges 6:09 into the third and less than 2 minutes later P.K. Subban provided some insurance on the power play.
Montreal maintained a one-point lead over Boston in the Northeast Division after the Bruins defeated Toronto Thursday.
Carolina, which had a four-game winning streak snapped, began the evening with a six-point advantage over Winnipeg and Tampa Bay in the Southeast Division.