As the celebration was starting, the Montreal Canadiens recalled that they are still four wins short of their goal.
"A lot of us haven't been this far before," Muller said. "We worked hard for it, but we know we'll have to get right back to work."
The Canadiens won the best-of-seven Wales Conference final, four games to one, and earned a rest before the championship round. Montreal will seek its 24th Stanley Cup title in a series beginning June 1 against the winner of the Campbell Conference final, the Kings or the Toronto Maple Leafs.
"It's a team goal and this is just the third step," forward Brian Bellows said. "I'm excited, but I won't get overly dramatic about tonight. We've still got a long way to go."
The Canadiens exchanged hugs and smiles but refused to ham it up too much after receiving the conference championship trophy.
The Canadiens, who won twice in overtime in the series, were determined not to return to New York for a sixth game against the Islanders, who had already come back twice to upset the Stanley Cup champion Pittsurgh Penguins in the Patrick Division final.
The Canadiens had a record-tying 11-game playoff winning streak ended Saturday night in New York when the Islanders forced a fifth game with a 4-1 victory.
"We had a good talk this morning before our skate," Bellows said. "We said tonight's the night. We have to do it. We can't let it get any longer."
Winger John LeClair, whose hitting and aggressive forechecking set the tone for Montreal, added: "We got the team effort we didn't get in Game 4. We definitely didn't want to go back to New York."
New York forward Ray Ferraro saw the turning point come before Monday's game.
"If you want it in a nutshell, the two overtime games were the key," Ferraro said. "We had the chances and didn't score in them."
Muller and Mike Keane scored in the first period for Montreal, and Bellows, Damphousse and Jean-Jacques Daigneault added goals in the second. Steve Thomas scored for the Islanders in the second period and Benoit Hogue got a goal in the third.
A Forum crowd of 17,959 at Montreal began chanting in the second period after Bellows' goal made it 3-0. "It sure feels great," Bellows said. "We had the killer instinct tonight."
It will be the Canadiens' first trip to the final since 1989, when they lost in six games to the Calgary Flames. Montreal last won the Cup in 1986.
Muller scored 58 seconds into the game after some aggressive forechecking by LeClair. Muller skated out of the corner to backhand a shot between goaltender Glenn Healy's pads.
Muller took a hit from Darius Kasparaitis and shoveled the puck to Keane in front for a high shot from close range with LeClair blocking Healy's view at 17:11.
Damphousse was left uncovered on the left side on a rush to take Stephan Lebeau's pass and beat Healy on the stick side with a low wrist shot 1:58 into the second period.
Daigneault scored on a long, screened wrist shot at 15:02 and Bellows got another only nine seconds later from the slot.
The Islanders stormed into the Montreal zone and, after a long scramble, Thomas put his ninth goal of the playoffs behind goaltender Patrick Roy from in close on the left side.
Hogue scored on a screened drive from the left side 3:46 into the final period.
The Canadiens outshot the Islanders, 33-28.