The Danish centre scored in the first period and added the decisive goal in a shootout Wednesday as the Canadiens stretched their winning run to four games with a 4-3 victory over the Ottawa Senators.
Eller had been Montreal's best and hardest-working player all night, and he came through with the game-winner after Alex Galchenyuk and Jakob Silfverberg had traded goals during the first two rounds of the shootout.
"You want that chance to win it for your team, you want that responsibility, so it feels good right now," said Eller, who had seven of Montreal's 45 shots on Ottawa goalie Robin Lehner in regulation and overtime.
"It's good for this team that we can win all types of games. We can defend leads, we can catch up if we're behind. We won in a shootout this time. It's good for the team's confidence."
Brendan Gallagher and P.K. Subban had power play-goals in the second period for Montreal (18-5-4), which retained first place in the Eastern Conference despite some loose play in its first game at home after a five-game road trip.
Mika Zibanejad and Daniel Alfredsson had power-play goals for Ottawa (13-8-6), while Patrick Wiercioch also scored for the Senators, who are 1-2-4 in their last seven.
In the shootout, Eller used a drag move and lifted the puck over Lehner to put Montreal ahead and Carey Price then stopped Kyle Turris to end the game.
It was the third time in Ottawa's last five games that Lehner was on the wrong end of a shootout decision.
"I can't seem to find a way in the shootout and I'm a little tired of the one-point games," said the 21-year-old Swede. "Our guys are playing their hearts out and they deserve the two points.
"It feels good in the regular game and the overtime, but when it comes to the shootout, right now I'm not there. It's another speed. It's not the AHL any more. It's something I've got to work on because it's not working now. It sucks."
There was disappointment that Senators forward Kaspars Daugavins wasn't picked as one of Ottawa's three shooters. The Latvian was the talk of the NHL for his failed shootout attempt in a 3-2 loss to Boston on Monday in which he skated in with the puck pinned on the end of his stick and then made a turn-around move.
Coach Paul MacLean said Daugavins would have been his fourth shooter if one was needed and that the player "had something special again" in mind for his attempt. But he never got the chance to use it.
The result gave the teams two wins each in their four-game season series.
Wiercioch, a rookie defenceman, scored his third goal in the last five games after not scoring in his first 26 in the NHL to tie things 3-3 early in the third.
With a goal and an assist, Subban has points on Montreal's last nine power-play goals.
The Canadiens opened the scoring as recent callup Gabriel Dumont earned his first NHL point as he worked the puck from behind the net to Eller, who lifted it over Lehner at 7:02 of the first period.
An Ottawa power play was nearly over when Silfverberg made a sweet pass from a crowd in the corner to Zibanejad, who beat Price with a quick wrist shot to tie it at 10:26.
Pacioretty skated in off the boards and slipped a shot between Lehner's pads 6:40 into the second and Subban scored from the point on a shot that hit Ottawa defenceman Chris Phillips in front at 17:21.
Time was about to expire in the second period when Alfredsson aimed a shot over Price's shoulder that hit the camera inside the net and bounced out. Video replay confirmed the goal at 19:58.
Wiercioch tied it 1:50 into the third when he moved across the blue-line, put a move on Andrei Markov and scored on a wrist shot from the slot that beat Price between the legs.
The Canadiens were coming off a road trip in which they took eight of a possible ten points by winning in many different ways and finding different ways to score. It was their eighth straight game with at least three goals.
"I don't think we played our best game tonight," said Montreal defenceman Josh Gorges. "But we did good things when we had to.
"We cycled the puck in the offensive zone and got pucks in front of the net. I think we were sloppy at times though. Our penalty killing has to be better. We got loose in a few areas. But coming back after a long trip, we did what we had to do to get the two points."
Notes: The banged-up Senators are still without Craig Anderson, Erik Karlsson, Jason Spezza, Jared Cowan and Milan Michalek. Peter Regin didn't dress. ... UFC star Georges St-Pierre got a big ovation as he dropped the puck for the ceremonial faceoff. ... The Montreal Impact's new Swiss coach, Marco Schallibaum, attended the game, although the Canadiens' Swiss players, Rafael Diaz and Yannick Weber, are both out with injuries. ... Following the game, the Canadiens returned defenceman Greg Pateryn to the Hamilton Bulldogs of the American Hockey League.