Panarin extended it to 3-0 at 12:49 of the second period after scoring from the high slot.
Peterka cut it to 3-1 at 18:30, scoring from the left circle into the top of the net following a shot from Owen Power that was blocked by Rangers defenseman Jacob Trouba.
The Sabres tried to make a push in the third period, but the Rangers blocked 13 shots.
“I think it's fun, honestly,” Trouba, New York's captain, said of blocking shots. “A lot of guys get excited about it. It's fun to contribute and do things like that. It takes some courage. It's not for everyone, but when you have guys that are willing to do it, it kind of goes through the team.
“And it's kind of an attitude that we want to establish early, kind of a culture, and I guess what makes our team us is that passion, that energy and that spreads throughout the locker room.”
Kreider put the Rangers ahead 4-1 at 11:34 of the third with a short-handed goal, scoring on a pass from Zibanejad at the front of the net.
Trouba scored into an empty net at 18:31 for the 5-1 final.
“We’ve obviously struggled against the 1-3-1 (defense) in the past and we’ve got to figure out how to play a simpler game when we play it, because we just overcomplicated it tonight,” Sabres captain Kyle Okposo said.
NOTES: The Rangers are 11-0-3 in their past 14 games against the Sabres. … Fox’s assist was the 200th in 286 NHL games, making him the sixth-fastest defenseman in League history to reach the feat and second-fastest for New York (Brian Leetch, 264 games). … Shesterkin became the seventh-fastest goalie in NHL history to reach 100 wins (154 starts). … Zach Benson (18 years, 153 days) had two shots in 14:27 of ice time in his NHL debut, and became the second-youngest Sabres player to play a regular-season game after Pierre Turgeon (18 years, 41 days). … Levi (21 years, 289 days) was the youngest Sabres goalie to start a season opener since Tom Barrasso (21 years, 192 days) on Oct. 9, 1986. He’s the first rookie goalie to start for Buffalo in a season-opening game since Ryan Miller on Oct. 5, 2005. … Prior to the game, longtime broadcaster Rick Jeanneret, who died in August at 81, was honored, renaming a stretch of road in front of the arena to “RJ Way” and with a video tribute. His family also participated in a ceremonial puck drop. The team will wear an “RJ” patch on their jerseys all season.