Stafford scored 46 seconds into overtime to give the Sabres a 3-2 victory against the Minnesota Wild at the Xcel Energy Center.
Jason Pominville and Rob Niedermayer also scored to help Buffalo move into eighth place in the Eastern Conference, a point ahead of Carolina for the final playoff spot.
The Sabres are 6-0-1 in their last seven road games, the first time they've earned points in seven straight road games since opening the 2006-07 season by winning an NHL-record 10 straight away from home.
Stafford, who scored Saturday in a 5-3 victory in Philadelphia, picked up the puck at the Wild blue line, went around Brent Burns and tucked the puck under goalie Jose Theodore's leg.
"I was kind of at the end of a shift, so I didn't have too much left in me. I just tried going to the net and kind of pushed off of Burns," Stafford said. "I just kind of leaned into him and happened to get a lane to the net, went in and put it in."
Before this weekend, Stafford, who has a team-leading 26 goals in 47 games, was held without a goal in eight straight.
"No matter how focused you are or how are you're working, you're going to go through tough times. It's just a matter of how you respond," he said. "I felt as though I was sticking with it and getting chances and getting shots. They just weren't going in like before, but now, hopefully, I can pick it back up."
It was the fourth game of as seven-game trip for the Sabres, who have stops in Pittsburgh, Boston and Toronto before next Sunday's home game with Ottawa.
"From an effort standpoint, back-to-back and a tough turnover, I thought our third period, our battle and the amount of puck time we had in the offensive zone was real good," coach Lindy Ruff said.
Warren Peters and Marek Zidlicky scored for Minnesota, which has lost three of four. The Wild earned a point for advancing to overtime to move into a tie for ninth in the Western Conference with Anaheim and Nashville, a point behind eighth-place Los Angeles.
Andrew Brunette had a chance to win it for Minnesota late in the third period, but was stopped on a breakaway by Jhonas Enroth.
Minnesota coach Todd Richards said opportunities like that have to be converted.
"That's playoff hockey right now," Richards said. "The chances are really limited just because teams are putting a premium on defending."
Pominville scored 1:23 into the game on a perfectly executed a 3-on-1. He carried the puck into the Wild zone and passed across for Thomas Vanek, who left the puck for Steve Montador. The defenseman cut to his left and backhanded it across the crease to Pominville at the right post for an easy tap-in. It was his second goal in as many games.
Niedermayer slammed home a rebound of Andrej Sekera's shot at 2:04 of the second period for his first goal in 67 games.
Minnesota scored twice late in the period to tie it.
Peters charged down the slot to tip a centering pass from Brad Staubitz into the Buffalo net with 5:47 left, and Marek Zidlicky beat Enroth with a snap shot on a power play with 2:27 to go.
"I feel we left a point on the board," Brunette said. "I think we were sluggish in the first period, but I think we picked up the play after that and played better."
Theodore, who made 40 stops Thursday night at the Rangers and 46 saves Feb. 25 at Anaheim in his last two starts, made 30 saves for the Wild.
Material from wire services and team media was used in this report.
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