The Sabres were in position to steal the Eastern Conference title from the higher seed Carolina Hurricanes. Buffalo led Game 7 on the road in the third period before things fell apart.
Miller and the Sabres returned to hockey's final four Sunday and are ready to take the step they tripped over a year ago.
"It feels pretty good to be back where we feel we belong," Miller said.
Chris Drury had a goal and assist in the Sabres' four-goal second period that erased an early deficit and sent Buffalo to a 5-4 victory Sunday over the New York Rangers in Game 6 of the conference semifinal series. Miller preserved the win with 32 saves, including 11 in a frantic third period.
"I remember walking out of Carolina's rink talking to my dad, shaking my head and saying, 'I was 20 minutes away from a chance,"' Miller said. "It stuck with me the whole year. I want that chance again and I think everybody in this room appreciates it more that we got so close."
The only ones now standing in the way of the Presidents' Trophy-winning Sabres are the Ottawa Senators, Buffalo's Northeast Division-rival. These teams know each other well, and probably won't need much time to rekindle hostilities.
A late-February brawl in a game between the teams led to 100 penalty minutes. It was sparked by a hit on Drury.
"We definitely have some history with Ottawa and we're going to have to go out and play our best hockey, so far, to have a chance to win that series," Miller said.
Buffalo also eliminated Ottawa in last year's playoffs.
Hecht tipped in his second of the game -- and the playoffs -- with 5:10 left. Daniel Briere, co-captain with Drury, had three assists.
"Odd-man rushes," Jagr lamented. "We said that all series long. We just can't give it to them. ... We didn't lose it, we just gave it to them. They are a great team but they aren't better."
Nylander added his second of the game with the Rangers' third power-play goal of the game to make it 5-4 with 2:59 remaining. It just wasn't enough against the NHL's highest-scoring team.
Henrik Lundqvist stopped 24 shots for New York, which dropped its first home game in the playoffs (4-1) and had a nine-game Madison Square Garden winning streak snapped.
Miller jumped into a hug with defenseman Henrik Tallinder when the Sabres won the final faceoff and cleared the zone.
"I think there is a lot more hockey left in this club so we're going to have some fun," Miller said.
Drury again led the Sabres, who eliminated the New York Islanders in the first round and are shooting for their first Cup title after posting the league's best regular-season record.
He tied Game 5 by scoring with 7.7 seconds left in regulation to keep the Rangers from a third straight win that would've given New York a chance to end the series the other way Sunday. Maxim Afinogenov won it for Buffalo in overtime and set up the clincher.
The Sabres have a chance to erase last year's bitter memories. They will have home-ice advantage against Ottawa.
"We always had our focus and our energy," Drury said. "I think when you have an attitude like that things kind of just build on themselves."
New York's lead was lost quickly when Kalinin tied it at 1:29 of the second. Kalinin took a pass from Ales Kotalik at the left point and wound up for a shot as New York forward Nigel Dawes dived in front to block the puck.
The Rangers rookie, a surprise addition to the lineup Sunday, got a piece of it. That sent the puck knuckling past Lundqvist to make it 1-1.
It was the jolt the Sabres needed to get Lundqvist off his game and send them into a full press. Buffalo outshot New York 11-8 in the first period, but the margin was much larger before Nylander broke through with 2:50 left in the period.
That was forgotten when Pominville gave the Sabres their first regulation lead since midway through the third period of Game 2. Again a deflection proved costly to the Rangers as Pominville's shot hit defenseman Karel Rachunek before darting past Lundqvist at 2:53.
Mara restored the faith into the nervous Garden crowd when he fired a shot in from above the right circle to tie it at 2, just 1:47 after the Rangers fell behind. The goal came on New York's first power play of the game after going 0-for-7 in Game 5.
Balloons again filled the arena that soon became quiet enough to hear them pop along with the Rangers' hopes of reaching the conference finals for the first time since 1997.
On a 3-on-2 rush, Hecht took a pass from Drury in the left circle and sent it hurtling over Lundqvist's left shoulder to give Buffalo a 3-2 lead at 7:41.
"I felt I was there all the time," Lundqvist said. "I just got beat by a couple of weird plays."
Drury then got free in front during a power play and took a pass from Briere and scored 3:34 later.
The Rangers held a 15-11 shots advantage in the second period, but that was the only highlight of the frame that ultimately ended their season.
- Dawes, who played in eight regular-season games, replaced LW Brad Isbister.
- Drury was in line for his 15th winning goal in the playoffs before Nylander scored again.
- The teams combined for 14 goals in Games 2-5, with the previous three ending 2-1.