Leino scored twice in the first 3:44 and Miller made 32 saves to help the Sabres beat the NHL-leading Vancouver Canucks 5-3 on Saturday night.
Leino had gone 14 games without a goal. The 31-year-old forward was one of Buffalo's prized free-agent acquisitions, inking a six-year, $27 million deal, but has struggled mightily with 20 points in 60 games.
"It's been a tough season," Leino said. "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, dealt to Vancouver along with Marc-Andre Gragnani in exchange for Cody Hodgson and Alexander Sulzer at the trade deadline Monday, scored his first goal for the Canucks and added an assist while playing mainly on the second line with Ryan Kesler and David Booth.
"It was nice to get the goal, maybe get the pressure off my back," Kassian said. "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, former Canuck Christian Ehrhoff and Tyler Ennis also scored for Buffalo, while Miller had his shutout streak stopped at 155:37. The Sabres, 6-0-2 in their past eight games, moved within two points of eighth-place Winnipeg in the race for the final playoff spot in the Eastern Conference.
"We're battling hard to get back in the picture," Sabres coach Lindy Ruff said. "When you can beat a team that's basically the first-place team in the league, it's a big plus."
Booth scored twice for Vancouver. The Canucks lost in regulation for only the second time in the past 21 games.
Buffalo chased Canucks goalie Roberto Luongo from the game early.
Hodgson received warm applause when it was announced he would start the game, as well as the first few times he touched the puck. The Canucks held their former third-line center in check, but his teammates had free reign in the first period as they built a 3-0 lead.
Kassian's goal with 2:46 remaining in the third period, a wrist shot from the slot that beat Miller up high, made it 4-3 as Vancouver nearly made a comeback.
But Ennis iced it with an empty-net goal.
Earlier in the third period, Ehrhoff scored the winning goal.
Ehrhoff, who spurned a five-year, $23 million offer from Vancouver in favor of Buffalo's 10-year, $40 million pact, had his point shot go off Aaron Rome's leg and in to make it 4-1 for his fifth of the season.
Booth responded shortly after, backhanding Kassian's rebound behind Miller for his 100th career goal.
The game was perhaps Leino's best for Buffalo.
"I told Ville after the game he's a better shutdown guy than he is a scorer," Ruff said. "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 game, Leino one-timed a shot through Luongo's legs. Less than 3 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 signaled a goal, so play went on for another 2:08 -- including Henrik Sedin's 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," Luongo said. "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. He finished with 16 saves on 17 shots.
His only blemish was Ehrhoff's goal.
Miller was just shy of beating his career-best shutout streak of 161:36. ... Buffalo had gone 0-6 in Vancouver since its last victory on Feb. 28, 1999.