The Devils, 0-11 this season in shootouts, are three points out of the Eastern Conference's final wild-card spot.
"We had a bunch of chances to score and we have guys who are good in the shootout," Zubrus said. "Tough to say it's luck because it's been 11 games in a row, but maybe a bit of bad luck has to be there."
The Devils outshot Buffalo 10-8 in the opening period, and New Jersey broke the deadlock in the second, when Michael Ryder's cross-crease pass appeared to be knocked into the Sabres' goal by Jamie McBain. The goal was awarded to Zubrus.
Lieuwen returned to form after the goal, making a diving stick save on Ryder to keep the score 1-0. Moments later, he stopped Ruutu on a partial breakaway.
"The one word that Teddy keeps using is compete," Lieuwen said. "I just went out there and competed. Good things happened."
The Sabres managed just four shots in the second period.
Buffalo got the equalizer 1:39 into the third period on a play started by Drew Stafford and completed by a cross-slot pass from Leino to Ennis, who scored on a wrist shot to become the first Sabres player to score 20 goals this season.
"He's a dynamic player," Nolan said. "He scoots in and out, and for him to get that 20, it's a magical number he was waiting on for a while."
Buffalo took its first lead of the night on a power play just more than three minutes later. Cody Hodgson slid a pass through several players to Ennis, who shot high into the net at 4:41.
"He made a pretty ridiculous pass through two or three guys right on my tape," Ennis said. "I just had to throw it on the net."
New Jersey tied the score on the power play, when Ruutu deflected Greene's shot past Lieuwen.
He then had a chance to win the game after Stafford scored in the fourth round of the shootout.
"I had a 'Welcome to the NHL' moment when (Jaromir) Jagr came down on me with a chance to win the game and I think I was a little too excited about what was happening," Lieuwen said.
But after Leino scored, Lieuwen rebounded to pick up that first win with a stop on Mike Sislo that he doesn't quite remember.
"I blacked out," Lieuwen said. "The guy came in, and as soon as I made that save, I was just all smiles. I was excited and I'm very grateful."
Buffalo snapped a four-game skid with the win, while the Devils now have points in five consecutive games.
Stafford was selected the Sabres' Masterton Trophy nominee by the Buffalo chapter of the Pro Hockey Writers Association earlier Tuesday. ... New Jersey LW Ryane Clowe missed the game with a head injury sustained Monday against Florida. ... Buffalo signed 2012 third-round pick Justin Kea to a three-year, entry-level contract before the game.
Copyright by STATS LLC and The Associated Press
BUFFALO, NY - APRIL 01: Goaltender Martin Brodeur #30 of the New Jersey Devils looks on while warming up for their...