Eller first faked a backhander, then switched to his forehand to fire a shot past Robin Lehner. Montreal's Carey Price followed by stopping Kyle Turris to clinch the victory, the Canadiens' fourth in a row.
Eller also opened the scoring 7:02 into the first period with his fourth of the season and Montreal took a 3-1 lead late in the second on a power-play goal from P.K. Subban.
Toronto fought back, however, when Daniel Alfredsson scored on the power play with 2 seconds left in the middle period. Patrick Wiercioch tied it for the Maple Leafs early in the third.
Price stopped 29 shots to get the win. Ottawa suffered its sixth loss in seven games with Lehner making 42 saves.