Stafford scored the go-ahead goal with 5:26 left and assisted on Nathan Gerbe's game-winner 2:04 later in a 4-3 win over the road-weary Edmonton Oilers on Tuesday night.
The Sabres won for only the second time in eight games (2-5-1) and sixth time in 20 (6-10-4).
"We've talked about it enough. Bottom line is guys knew we just needed to go out there and get it done," Stafford said. "It feels good to get those two points. Now, hopefully we can string a few together."
Stafford's three points on Tuesday matched his production — three assists — in his previous seven games. He helped spark an offence that had produced two or fewer goals in 13 of 20 games.
Stafford snapped a 2-2 tie by tapping a loose puck at the net that dribbled between goalie Nikolai Khabibulin's legs.
"I kept whacking at it, and finally got one, got a break," Stafford said. "It's nice to finally get rewarded with a break."
Gerbe put the game away by streaking up the left side, cutting to the net and shovelling the puck just inside the right post.
Jordan Leopold and captain Jason Pominville, who played despite an illness that limited his ice time, also scored for Buffalo. Ryan Miller made 23 saves to improve to 6-0 against Edmonton.
Corey Potter brought the Oilers within 4-3 with 1:50 left, but Edmonton didn't get off another shot. Sam Gagner had a goal and assist, and Taylor Hall also scored for Edmonton, 1-4 during its seven-game trip.
The Oilers fell back into their losing ways one night after a 4-3 win at Chicago that snapped a seven-game road skid.
Oilers coach Tom Renney remained upbeat and praised his young and banged-up team for showing resilience.
"We gave Buffalo everything they could handle. It was a winnable game for us," Renney said. "We were very passionate, and we really tried to play within our structure. We didn't quit, and that's as important as anything."
The Oilers got off to a flying start despite playing on back-to-back nights and missing NHL rookie scoring leader Ryan Nugent-Hopkins, who is out indefinitely after hurting his left shoulder on Monday.
Buffalo was outshot 9-0 before Gerbe got a puck on net with a spin-around backhander from the right circle that Khabibulin kicked away with his right pad nearly eight minutes in.
The Oilers had a 12-2 shots edge when Hall opened the scoring by snapping a shot from the left circle off the right post to cap a 3-on-2 rush 10:33 in.
As quickly as the Oilers started, their offence petered out as they managed two shots the rest of the period.
Khabibulin didn't look sharp in allowing Pominville to score on a bad-angle shot from the right circle with 5:37 remaining in the first.
The teams traded goals in the second period, though the Oilers also had one disallowed.
Potter scored on a slap shot from the right point, but the goal was negated because Ales Hemsky was penalized for goalie interference. Hemsky was working his way across the top of the crease when he nudged Miller.
"I don't think so," Hemsky said, arguing that it appeared to him that Miller was already on his way down when they touched.
"He glanced off Miller," said Renney, questioning whether the goalie embellished the hit. "It's not Miller's first rodeo, and down he goes."
The Sabres (18-17-4) avoided falling under NHL .500 for the first time since Jan. 13, 2011, when they were 19-20-5.
Sabres coach Lindy Ruff was impressed by how his players drove to the net to produce opportunities.
"We've been talking about the inside ones, and I said, 'We're going to have to get some guys around the crease ... and jump in,'" Ruff said. "It's nice to score some goals."
Stafford wasn't one to complain about how the goals went in, or how slowly the Sabres started.
"We're not looking for a perfect game," Stafford said. "We're looking for wins."
NOTES: Nugent-Hopkins watched from the press box with his shoulder in a sling. He is expected to travel with the team for Thursday's game at St. Louis, before being re-evaluated by doctors this weekend. ... A knee injury to Oilers D Tom Gilbert is not as bad as expected. Renney expects Gilbert to resume skating as early as Wednesday. Gilbert was crunched into the boards by Chicago's Daniel Carcillo. ... The Sabres improved to 8-2-2 this season against Canadian-based teams.Suggest a correction