Visnovsky, who was second on the team in scoring with seven points, suffered a lower back strain in the second period. Palffy, the Kings' scoring leader with 12 points, took a hard hit from Buffalo's Adam Mair in the first and did not play the final 20 minutes because of a cervical sprain.
The Sabres had two power-play tallies in the first period, an even-strength goal midway through the second, and a shorthanded score in the final minute of the period.
The Sabres improved to 2-2-0 on their six-game road trip.
Derek Armstrong tallied for Los Angeles, which fell to 2-2-0 on its seven-game homestand.