It was Luukkonen’s first shutout of the season and his eighth in the NHL.
Josh Dosh and Josh Norris scored for the Sabres (42-20-6), who are 10-1-0 since returning from the Olympic Break.
Buffalo moved into a tie with the Carolina Hurricanes for first place in the Eastern Conference. Carolina, which lost 5-1 to the Columbus Blue Jackets on Tuesday, has one game in hand.
Adin Hill made 23 saves for the Golden Knights (31-23-14), who had won two in a row.
Vegas dropped to third in the Pacific Division, one point behind the Edmonton Oilers and Anaheim Ducks. Edmonton, which has played one more game, defeated the San Jose Sharks 5-3 on Tuesday.
Doan gave the Sabres a 1-0 at at 18:02 of the first period. Hill went to play a dump-in behind the net, but he couldn't control the puck, and before he could back into his net, Doan banked a shot in off his right pad.
Norris added an empty-net goal at 19:02 of the third period for the 2-0 final.
