Leino scored twice in the game's first 3:44 and Miller was solid, finishing with 32 saves, as Buffalo chased Roberto Luongo from the game early en route to a 5-3 victory over the Vancouver Canucks.
"It's been a tough season," said Leino, the prized free agent who had gone 14 games without a goal. "It hasn't gone my way and it hasn't gone the team's way. But there's still a chance to make the playoffs and have fun here at the end. These are the games you want to play, when things count. And obviously every game counts now."
Kassian, who was traded to Vancouver along with Marc-Andre Gragnani in exchange for Cody Hodgson and Alexander Sulzer at the trade deadline on Monday, scored his first goal as a Canuck and added an assist while playing mainly on the second line with Ryan Kesler and David Booth.
He outduelled Hodgson, who still has a place in Vancouver fans' hearts. Hodgson was greeted with applause when it was announced he would start the game, as well as the first few times he touched the puck.
But when Kassian started banging bodies, then earned his first assist as a Canuck and followed it up with his first goal, the cheers for him were deafening.
"It was nice to get the goal, maybe get the pressure off my back," said Kassian. "But my mindset coming to the rink was about getting the two points. It wasn't about me or Cody coming back, it was about winning the game and we didn't do that tonight, so that's tough."
Brad Boyes, ex-Canuck Christian Ehrhoff and Tyler Ennis, into an empty net, also scored for Buffalo and Miller had his shutout streak stopped at 1:55:37 as the Sabres (30-27-8) moved to within two points of eighth-place Winnipeg in the race for the final playoff spot in the Eastern Conference.
The Sabres improved to 6-0-2 in their past eight games and can taste the playoffs after a dismal start to the season.
"We're battling hard to get back in the picture," said Sabres coach Lindy Ruff. "When you can beat a team that's basically the first-place team in the league, it's a big plus."
David Booth, with two, had the other goals for Vancouver (41-17-8), which lost in regulation for the second time in the past 21 games.
Kassian's goal with 2:46 remaining, a wrist shot from the slot that beat Miller up high, made it 4-3 as Vancouver tried to make a comeback from an early 3-0 deficit.
But Ennis iced the contest after Booth turned the puck over at centre ice.
Earlier in the third period, Ehrhoff scored the winning goal.
Ehrhoff, who spurned a US$23-million, five-year offer from Vancouver in favour of Buffalo's $40-million, 10-year pact, had his point shot go off Vancouver defenceman Aaron Rome's leg and in to make it 4-1 for his fifth of the season.
Booth responded shortly after, backhanding a Kassian rebound behind Miller for his 100th career goal.
Leino, who had gone 14 games without a goal, was the story to start the game.
The 31-year-old was one of Buffalo's prized free-agent acquisitions in the off-season, inking a US$27-million, six-year deal, but has struggled with 20 points in 60 games.
Saturday was perhaps his best game as a Sabre.
"I told Ville after the game he's a better shutdown guy than he is a scorer," said Ruff. "Ever since we've put him in a shutdown line, he's played well. I thought Ville played a great game. .... He deserved what he got."
Fifty-five seconds into the contest he one-timed a shot through Luongo's legs, and less than three minutes later he banged in a rebound after Luongo lost his stick and batted a rebound into the slot.
Boyes, left alone in the slot, made it 3-0 at 5:10 with a perfect shot that hit the post and barely crossed the goal-line. Nobody signalled a goal, so play resumed for another 2:08 -- including a Henrik Sedin breakaway that Miller stopped -- before the whistle blew and a video review showed the puck crossed the goal-line.
That was it for Luongo, who allowed three goals on seven shots.
"It was a bad start," said Luongo. "I got to be better than that for my teammates. The boys battled hard to try and come back, and played a pretty good match so obviously I'll take the responsibility for this one."
Cory Schneider drew loud applause when he entered, and finished with 17 saves.
His only blemish was Ehrhoff's goal.
NOTES: Miller was just shy of beating his previous shutout streak of 1:61:36. ... Buffalo had gone 0-6 in Vancouver since its last victory on Feb. 28, 1999. ... Gragnani finished minus-2 and was part of the first power-play unit. ... Chris Tanev sat for the second straight game to make room for Gragnani. Dale Weise was also a healthy scratch.