The 28-year-old hadn't started a professional game since March 7, 2020, with Cincinnati of the ECHL, making 24 saves in a 1-0 shutout against Toledo.
"It's super exciting," Houser said. "I'm not really in that great of game shape either, I'll admit that. So, I was like after the game celebrating and everything, I could barely breathe, so I'm just trying to catch my breath right now. [I'll] give my parents a shout after this and see what their take is on it."
Sam Reinhart deflected a Rasmus Ristolainen point shot to make it 3-2 at 15:56 of the third period, then made it 4-2 with an empty-net goal at 19:08.
Tage Thompson had a goal and an assist for the Sabres (14-32-7), who trailed 2-0 in the second period but ended a four-game losing streak.
"After I saw [the empty-net goal] went in, it was a huge relief," Houser said. "It's so exciting, like, I've worked my whole life for this, for it to happen. Just to play a game it's really special, but to win, winning's always the goal. That's why we play."
Semyon Varlamov made 36 saves but had his shutout streak end at 248:00 for the Islanders (31-16-5). Adam Pelech had a goal and an assist.
The teams play here again Tuesday.
"I thought we played, and I'll use a term I used with the players, I thought we played with a little bit of arrogance," New York coach Barry Trotz said.
The Islanders clinched a berth in the Stanley Cup Playoffs on Saturday but fell to fourth place in the MassMutual East Division following the Boston Bruins' 3-0 win at the New Jersey Devils on Monday.
"Even though we clinched a playoff spot and had an emotional weekend, that's not an excuse," Pelech said. "We're definitely disappointed with how we played, and we're aware of that. I thought we came out sluggish today when this is an opportunity to fight for positioning in the standings, play for home-ice advantage. We just we didn't play our game tonight and we need to get back to it tomorrow."