But it took until the playoffs for the Canadiens to find the balanced attack they have sought all season.
Getting offensive production from all four forward lines has helped them win the opening three games of their first-round series against the Tampa Bay Lightning.
They can sweep the best-of-seven series with a win on Tuesday night at the Bell Centre.
"That's a big strength," Eller said Monday. "I can't stress how important it is to have everybody involved, everybody contributing."
Players who underachieved on attack all season, notably Eller and Bourque, have found new life in the post-season. It has helped the normally low-scoring Canadiens average four goals per game against the Bolts, who are missing top goaltender Ben Bishop to an arm injury.
Bourque, a two-time 27-goal scorer who had a dreadful campaign of only nine goals, has three in as many games in the playoffs while playing left wing with centre Eller and right-winger Brian Gionta.
Eller, who had 12 goals in 77 games including stretch of 24 games with only one assist, has two goals and shares the team scoring lead with four points with Brendan Gallagher and defenceman P.K. Subban.
The Eller line has produced five goals, one more than Gallagher's unit with Tomas Plekanec and Brandon Prust.
The top line of David Desharnais, Max Pacioretty and Thomas Vanek has scored only twice, but has combined for 29 shots in three games.
The fourth line of Daniel Briere with Michael Bournival and Dale Weise has only one goal, but it was a big one as Weise scored in overtime in Game 1.
"Right now we have momentum and we're riding that wave," said Eller. "We knew depth was going to be important and I think a big part of why we're having success is we have all four lines contributing in one way or another.
"I guess the playoffs are just bringing out the best in all of us."
The Lightning are aware they have dug themselves a deep hole.
Only three teams have ever come back from a three-game deficit to win an NHL playoff series, most recently the Philadelphia Flyers against Boston in the second round in 2010. The Canadiens are 31-0 when holding a 3-0 lead.
Tampa Bay had its best outing in Game 3 on Sunday night, but dropped a 3-2 decision. They thought they had a 2-1 lead in the second period, but Ryan Callahan's goal was waived off due to Alex Killorn's incidental contact on goalie Carey Price.
"That was obviously a tough one to swallow," said Lightning star Steven Stamkos. "A couple of calls didn't go our way.
"We can't dwell on it now. We realize the situation we're in. We just have to win one game. Our backs are against the wall. I'm pretty sure you're going to see a good effort from us. That’s our motto right now: Just win one, then let’s go back home and see what happens."
Some wondered if Stamkos would be fit to play after taking an accidental knee to the head from Canadiens defenceman Alexei Emelin late in the second period. He returned for the third, but admitted later he took a major whack to the head.
"I feel pretty good so, yeah, I'm expecting to play," he said. "I got tangled up with Prust there and slid in.
"I don't think Emelin saw me and I got a pretty good knee to the head. Now that I saw it, I don't think there was any intention or anything. It was just kind of a play that happens in a game."
Emelin and his defence partner Andrei Markov were given a day off as the Canadiens held a short practice at their suburban training centre at the same time the Lightning skated at the Bell Centre.
The talk was mostly about how all four Montreal lines have played well in the series, which is a surprise on a team whose first unit carried the attack for much of the season.
After Vanek was acquired at the NHL trade deadline, he, Pacioretty and Desharnais produced 20 goals in the last 18 games of the regular season.
"I'm not surprised," said coach Michel Therrien. "We have to play well as a team defensively and that includes our forwards and our defence.
"We have to stick to our structure, stick to the game plan. This is when we're at our best offensively. When we start running around, that's when we get in trouble. But a lot of credit goes to the players. They stick to the game plan and they believe in it. And they have a lot of fun to play in that structure because they get results."
Montreal's only area of concern is special teams. The power play that went 0-for-23 over the final eight regular season games has only one goal in 11 chances in the playoffs. They spent the time leading up to the series working on the power play, but it continues to struggle.
"The only thing we need to improve on is the power play," said Vanek. "We got some good chances again, but we've got to start burying our chances. It's something I'm sure we'll address and get better at."
The Lightning have two goals on six chances against Montreal's penalty killing, which was fourth best in the league in the regular season.
So far, the Canadiens have done enough at even strength to beat coach Jon Cooper's young Lightning. Now they hope to end it in four games.
As teams have always done in that situation, the Canadiens told each other the fourth win in the hardest to get.
"The first three were pretty tough, too," said Vanek. "Cliches are cliches. We enjoyed the win. Everyone felt good about it. Today's a new day. We'll get back to work and hopefully we can close it out."
Cooper's message was much the same — just win the next one.
"I'm not going to throw out all the cliches and 'let's win one for the Gipper' and all those little kinds of things," he said. "The reality is you can't win a series in one game.
"I truly believe there's not much more wrong that can go against us. At some point karma's going to come around and we just need it for one night. All of a sudden you just gotta win one and you win that one and everybody's back on a plane. Who knows what happens after that?"