GLENDALE, Ariz. -- Drew Stafford didn't see the goalie, but he found the net.
"I was just trying to get a screen shot through," Stafford said. "I was trying to shoot it through a hole, get it on net and it happened to sneak in."
Jordan Leopold also scored and Ryan Miller made 33 saves for the Sabres, who won for the fourth time in five games. Buffalo won its fifth straight against Phoenix.
"We're starting to gain a little ground," Sabres coach Lindy Ruff said.
Scottie Upshall scored for the Coyotes, winless in six overtime games this season.
"Our overtime record isn't what it needs to be and that's the frustrating thing," coach Dave Tippett said. "Fortunately, it's an Eastern [Conference] opponent where the extra point doesn't matter."
Stafford took a pass from Leopold and fired a wrist shot past Jason LaBarbera from the right circle to win it.
After a scoreless first period, Leopold blasted a rising shot from the point over LaBarbera's blocker to give Buffalo a 1-0 lead at 6:34 of the second. Leopold's power-play goal came eight seconds after Wojtek Wolski was sent off for tripping.
"We've been talking about it," Leopold said. "We know we have to collect some points and really get on a roll."
Upshall tied it at 12:31, scoring off a long rebound after Miller deflected Adrian Aucoin's hard shot from the top of the circles into the bottom of the left circle.
"I thought in the second period we started to turn it up and caught another gear," Upshall said.
The Coyotes had two power plays in the final seven minutes of the third, the last starting with 2:36 left. Phoenix hasn't scored a power-play goal in five games.
"We had a couple of plays we could have executed better, but that's kind of the way the game was," Tippett said. "There were shots bouncing around and I thought Miller played very well for them."
LaBarbera learned 90 minutes before the game that he'd be starting because Ilya Bryzgalov was out with flulike symptoms. ... The Coyotes are 2-0-9 in games decided after regulation, with both wins coming in shootouts. ... The Sabres have one power-play goal in each of their past four games. ... Coyotes D Ed Jovanovski was honored for having played in his 1,000th NHL game, at Dallas on Dec. 26. ... Leopold's goal was his first since he scored twice against Florida on Dec. 23. ... An announced crowd of 13,905 was boosted greatly by Sabres fans. ... Phoenix captain Shane Doan's eight-game point streak was snapped.