It's the first time Buffalo (46-21-8) has had 100 points in a season since 2009-10.
Jack Quinn and Tage Thompson each had a goal and an assist for the Sabres, who have won two straight after a three-game losing streak (0-1-2). Ukko-Pekka Luukkonen made 26 saves.
Brayden Schenn had a goal and an assist, Bo Horvat had two assists, and Ilya Sorokin made 29 saves for the Islanders (42-29-5), who were coming off an 8-3 loss to the Pittsburgh Penguins on Monday.
Krebs put Buffalo ahead 3-2 at 16:59 of the third period. Alex Tuch skated around the net before sending a backhand pass out front to Krebs, who one-timed it past the outstretched blocker of Sorokin.
Bowen Byram scored an empty-net goal at 18:17 to make it 4-2 before Schenn scored from the side of the net with two seconds remaining for the 4-3 final.
Quinn gave Buffalo a 1-0 lead with a power-play goal at 14:19 of the first period. Fresh off the bench, Quinn picked up the puck at the left point and skated it to the circle, where he scored with a wrist shot that beat Sorokin to the far side.
Anders Lee had a chance to tie it at 6:34 of the second period, but Luukkonen gloved his backhand attempt on a penalty shot.
Calum Ritchie did tie it 1-1 on a power play at 17:57 of the second. Schenn took a pass from Horvat at the right side of the crease and quickly sent a cross-crease feed to Ritchie for a backdoor tap-in.
Thompson put the Sabres back in front 2-1 at 2:40 of the third period. He received a pass from Josh Norris in the high slot and put a wrist shot blocker side on Sorokin for another power-play goal.
Lee tied it 2-2 at 13:39 when his backdoor pass for Horvat deflected in off the skate of Buffalo defenseman Owen Power.
