The win was just the second in nine games for the Senators, who also snapped a two-game losing streak. The defending Northeast Division champs came in with the third-fewest points in the Eastern Conference.
"We're not playing beautiful hockey ... we're just trying to find a way to win like we did today," Alfredsson said. "It's one game, but it's a very big game for us."
Schaefer's goal, which came with 7:11 left, was upheld after a replay review showed he didn't strike the puck with a high stick.
"Guys on the bench were betting that it would be called back the way things are going," Schaefer said. "Buffalo's a good team, and we had been struggling. If we didn't come out hard tonight, they would have taken it to us."
"I saw the puck go in all the way," Alfredsson said. "I saw the puck was never over the crossbar."
Phillips sealed the win with a short-handed, empty-netter that was shot from behind his goal line, generating a collective roar from the Senators bench.
"It was a great character win, but it doesn't mean an awful lot if you don't carry on and play that way more," Senators coach Bryan Murray said.
Ottawa goalie Ray Emery made 27 saves in his first start since a loss to Montreal on Oct. 31. He had been hampered by a sprained left wrist sustained eight days earlier in practice.
"It was a big win," he said. "We need to start turning things around and having a positive attitude and start thinking we can win games like that one."
"They're a good team, let's not forget that," Sabres defenseman Brian Campbell said. "We didn't want to let them off the hook, but it happened."
Briere gave Buffalo a 1-0 lead 5 1/2 minutes in after he corralled Ottawa defenseman Andrej Meszaros' errant clearing pass at the Senators blue line. Briere took two strides and let go a slap shot from the top of the right circle that beat Emery.
The Senators tied it 4 minutes later on the power play when Neil's wrist shot from the bottom of the left circle got by Buffalo goalie Martin Biron.
Vanek made it 2-1 with his team-leading 12th goal, converting a rebound after Emery stopped Drew Stafford's wrist shot from the right circle.
Spezza tied it at 2 with a power-play goal at 6:32 of the third, deflecting Meszaros' slap shot from the left point.
"We wanted to make sure we came out with a playoff mentality," Spezza said. "We scored some ugly goals, but that's what you have to do against these guys to get the win."
Biron made 19 saves and lost for the first time in five starts. He foiled breakaway attempts by Alfredsson and Antoine Vermette in the first period, and was helped in the second when Ottawa defenseman Anton Volchenkov's slap shot ricocheted off two Buffalo players before hitting the right post.
"They got two goals that were deflected and found their way in," Biron said. "Sometimes the bounces go their way."
The Sabres will play six of eight at home. ... These teams will meet again in Ottawa on Saturday night. ... Sabres G Ryan Miller skated lightly Wednesday morning. He has missed four games because of an abdominal strain. ... Buffalo D Toni Lydman sat out for the third time with a neck strain. ... Ottawa is 1-7 when falling behind 1-0. ... Senators forward Mike Fisher had two assists.