There's nothing ailing the Buffalo Sabres that a little good luck couldn't cure.
It was the second straight tie for Buffalo (0-2-2), which lost to Dallas in the Stanley Cup Finals last season and is off to its worst start since going 0-4-3 in 1990.
Green's goal with 4.6 seconds deflected off Buffalo defenseman Alexei Zhitnik's skate in front and took another wobbly left turn underneath Hasek on its way in.
"When things aren't going your way, those are the kind of things that happen," said Sabres center Brian Holzinger, who went sliding through the crease in a vain attempt to stop Hull's shot.
"We have to start getting more goals for Dom," said Holzinger, whose team was shut out in its first game of the season while allowing the Detroit Red Wings 44 shots, lost to Washington 3-2 and tied the Atlanta Thrashers 5-5.
Michal Grosek had sent Buffalo ahead 2-1 in the third period, but Green's goal forged a tie that fet like a loss to the Sabres and left the Coyotes feeling like lottery jackpot winners.
"Coming in here against the Dominator you know it's going to be low-scoring affair," said Phoenix goalie Bob Essensa. "We were very lucky to get the bounces in the last five seconds."
Luck turned against Phoenix when defenseman Deron Quint hit the post 58 seconds into overtime for the best chance to win.
Green said he needed all the luck he could get against Hasek, a two-time league MVP and Olympic gold medalist who has led the NHL in save percentage the last six seasons. "Against Hasek, you're not going to beat him on a clean shot," Green said. "You have to take what you can get against the best goalie in the world."
Hasek made 32 saves, including three in overtime. He was pulled by coach Lindy Ruff in the second period Saturday after allowing the expansion Thrashers four goals.
"There's nothing wrong with him," Buffalo coach Lindy Ruff said. "I don't think he's on top of his game, but I don't think there's anything wrong with him. That last goal was off Zhitnik's skate."
Grosek's goal at 3:39 of the third snapped a 1-1 tie. Grosek took a pass from Brown in the slot and fired a low 25-footer underneath Essensa, playing in his first game since he signed with Phoenix as a free agent Sept. 5. Essensa made 22 saves, including four in OT.
Buffalo was outshot 13-5 in the first period, but took a 1-0 lead with a goal on its third shot. Defenseman Jason Woolley passed out of the Sabres' zone to streaking Geoff Sanderson at center ice. Sanderson wheeled in the zone and passed to Holzinger, who one-timed the puck to Stu Barnes for the tap-in at 14:41.
Hasek snapped his glove out to rob Trevor Letowski with 3:21 left in the first period, smothering a two-on-one break.
"Both goals we gave up late in periods, and those are the type of things that will kill you," Ruff said.
Phoenix (2-1-2) ended a tough road trip that had them play three games in four nights.
"It was a good bounce at the end but we allowed ourselves the opportunity to get that good bounce," coach Bob Francis said.
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