Houser became the sixth goalie to start a game for Buffalo this season. Mark Jankowski, Dylan Cozens and Alex Tuch scored for the Sabres.
Drake Batherson had the lone goal for Ottawa, and Anton Forsberg stopped 30 shots.
Ottawa's first home game since Dec. 11 was played without fans because of COVID-19 regulations.
The Senators had been looking for a third straight win as they returned from a two-game road trip in Western Canada.
With the game tied at 1, the Sabres scored the go-ahead goal midway through the third period on a bizarre sequence.
It all started when Ottawa defenseman Erik Brannstrom ran Kyle Okposo into the boards right between the benches. Players from both teams headed into the melee, but play went on without a whistle.
Jankowski took advantage of the confusion, breaking in with Ottawa's Josh Brown trailing him, and beat Forsberg stick side while most everyone else on the ice was caught watching.
''I think everyone thought the whistle was going,'' Senators coach D.J. Smith said. ''We had a bunch of guys piling on each other in front of the bench and it was a real fluke play.''
Brown was frustrated with himself for losing the puck and not being more attentive.
''I kind of looked up ice, I saw there was a scrum going on,'' he said. ''I kind of assumed that maybe the whistle was blown and I didn't hear it or it was going to be blown. I had the puck, so I should have just got it in. Obviously, the whistle wasn't blown.
''We learn that as kids to play until you hear the whistle, so my fault for sure.''
Jankowski said he knew play hadn't been stopped and he took full advantage of the distracted Senators.
''I was forechecking so I didn't really see what was going on until I turned up ice and saw the whole thing at the bench there,'' he said. ''(Ottawa's defensemen) were kind of gliding up there a bit and I didn't hear the (referees) blow a whistle, so I was like, I'm going to see if I can get this puck. I lifted (Brown's) stick and took the puck and got lucky they didn't blow the whistle there.''
Tuch added some insurance for Buffalo with 40 seconds left, putting the puck into an empty net.
''I was pumped,'' Houser said. ''Any time you can seal it with an empty-netter and run out the last 40 seconds with a two-goal lead, I like our chances. It's much better than them buzzing around, 6-on-5, us only up a goal. It was more fun to play that last 40 seconds after (Tuch) buried that.''
Ottawa had an opportunity to tie the game late in the third with a power play, but couldn't beat Houser. The Senators went 1 for 5 with the man advantage.
''First of all, our power play has been really good so you're hopeful they can get that job done,'' Smith said. ''Our issue is we didn't get set up.''
Down 1-0 in the second, the Senators tied it with Batherson's first power-play goal of the season. Batherson took a pass down low and, after his initial shot was stopped, lifted his own rebound over Houser.
Houser got off to a great start with a big save against Alex Formenton on a breakaway and followed that up with a big stop on Tim Stutzle on the rebound.
''He was unbelievable tonight,'' Jankowski said about Houser. ''A few times there he bailed us out huge, especially in the first two periods there. He was unbelievable for us back there. We have the most confidence in him and he's just a great guy, someone that everyone in that locker room loves to battle for, loves to play in front of.''
Buffalo opened the scoring midway through the first period as Cozens got pushed off the puck on the rush but then picked it right back up and let a shot go that beat Forsberg glove side.
NOTES: Filip Gustavsson was recalled from Belleville of the AHL after Ottawa goalie Matt Murray became ill and was unable to dress due to an illness not related to COVID-19. ... Vinnie Hinostroza did not travel with the Sabres after getting injured Monday during an overtime loss to Detroit.
Sabres: Host the Dallas Stars on Thursday night.
Senators: At the Pittsburgh Penguins on Thursday night.
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