Hammond made 24 saves, and the Senators (29-23-11) continued their push for a berth in the Stanley Cup Playoffs from the Eastern Conference. Ottawa trails the Boston Bruins by three points for the second wild card.
The Senators were 14 points out of a playoff spot on Feb. 10.
The Sabres (19-41-5) took a 2-0 lead in the first period when Philip Varone and Tyler Ennis scored, but the Senators took advantage of Buffalo's inexperienced defense and came back when Erik Karlsson scored early in the second period, and Mika Zibanejad and Mark Stone scored early in the third.
"We were fortunate to get the win," Hammond said. "I think it started with me. I don’t think I had my best game, by any means. Seemed like I was just fighting it all night, and for a while there it translated to the team.
"At the start of the second period we had a good push-back, and the third as well, to get the goals. From there it was just kind of trying to will the rest of the game and just play an ugly style of hockey. Fortunately we were able to."
Buffalo goaltender Chad Johnson, who was acquired at the NHL Trade Deadline from the New York Islanders, was supposed to make his Sabres debut, but he sustained an injury during the morning skate and could miss the rest of the season, Sabres coach Ted Nolan said.
"Chad unfortunately hurt something lower body and he’ll be out for a while. It’s not day-to-day. It will be for a while," Nolan said.
Zibanejad and Stone scored 1:34 apart early in the third period.
Stone gave the Senators the lead with his 16th goal at 3:08 when he jumped into the crease to score on a rebound after a Milan Michalek wraparound.
Stone said Karlsson’s goal, which gave him the scoring lead among NHL defensemen at 50 points, allowed the Senators to settle down.
"It wasn’t quite our best in the first, but at the same time I don’t think we played our worst. We were still getting chances in the first, but to come out in the second and get that early goal really gave us a sigh of relief, the comfort level we needed to go forward," Stone said.
"I think we’ve gained almost 11 points in the last month. It’s been fun. We’re enjoying coming to the rink every day and being around each other. You just kind of do it for the guy sitting beside you. It’s been a fun roll and hoping to continue the success we’ve been having."
Varone, who also had an assist on Ennis’ Sabres-leading 16th goal, and said Buffalo let Hammond and Ottawa off the hook.
"I played against [Hammond] a few times [in the AHL]. He’s a great goalie," Varone said. "I’m happy for him. He deserves to be here, but I think we had him on the ropes a little bit. [Ennis] hit the post there [when it was 2-0] and it looked like we should have more control of the game and our foot was off the gas."
The Senators made it 2-1 26 seconds into the second period when Karlsson scored his 16th goal. Buffalo had a couple of chances to get control of a puck that was going back and forth along the end boards before it went out to Karlsson at the right point.
Karlsson’s wrist shot made it to the edge of the crease where it bounced off the leg of Sabres defenseman Zach Bogosian and into the net to the right of Lindback.
Varone was leading Rochester in scoring when he was recalled by the Sabres for the third time this season Feb. 26. He showed some speed on his goal, chasing down a puck that was chipped toward the Ottawa goal and beating Hammond and Senators defenseman Marc Methot to the puck.
As Hammond attempted to swipe it away, Varone got his stick on the puck first and knocked it into the net at 7:22 of the first period.
Ennis took advantage of a screen to put the puck behind Hammond at 16:32 of the first period.
It was the 14th time in 65 games the Sabres led after the first period this season. They are 8-6-0 in those situations.
"We had a 2-0 lead; it was a good experience for us to go through trying to protect that lead, try to hang on. We just didn’t do it this time," Nolan said.
"We just didn’t have enough. We give what we have to give and at the wrong time they just outskilled us in certain situations. They beat Ristolainen back to the net on that first goal. Varone didn’t get his stick on the puck, trying to just put your stick out there … this league is a very tough league to try and defend against some of the top players, and right there they got a good lesson."
Buffalo plays the fourth game of a five-game road trip Saturday at the Washington Capitals, and Lindback said he wants the chance with Johnson injured.
"I feel good. This is what I’ve been working for for a long time to get some play time and try to prove myself," he said. "Obviously, that’s disappointing today, but I’m ready and I want to get back in there tomorrow and try to win that game."
Ottawa plays the second of its three-game homestand Sunday against the Calgary Flames.