Thompson gave Buffalo a 1-0 lead at 1:21. Cozens won a face-off in the left circle to Thompson in the high slot, and he scored bar down on a 5-on-3.
Olofsson extended it to 2-0 at 9:56 on a one-timer from the left circle.
"The second goal was a chip in, simple, puck behind the opponent's net," Sabres coach Don Granato said. "Right away, [Rasmus] Asplund jumps in, change sides behind the net, Victor Olofsson's open. And so, we pushed depth, we changed sides, which causes coverage change, find a pocket, and that was a very, very big goal in how it happened. That was something we weren't willing to do enough early on. And then obviously, that opened up the game."
JJ Peterka scored 13 seconds later at 10:09 to push it to 3-0 when he finished at the right post after receiving a give-and-go pass from Jack Quinn.
The Kings have allowed consecutive goals in under 30 seconds in two of its past four games, including 26 seconds apart against the Maple Leafs. They also allowed two goals in 1:31 in a 6-5 overtime loss to the Columbus Blue Jackets on Sunday.
"I don't know if I can pinpoint anything," Los Angeles captain Anze Kopitar said. "Bottom line is, we've got to figure it out and not allow that to happen."