Fiala, a forward, was acquired by the Kings in a trade with the Minnesota Wild on June 29 and signed a seven-year, $55.125 million contract ($7.875 million average annual value) the next day.
He tied it 1-1 for Los Angeles at 14:07 of the second period, then assisted on Adrian Kempe's power-play goal at 1:48 of overtime for the 2-1 final.
Cal Petersen stopped 10 of 11 shots in the first period for the Kings, and Pheonix Copley stopped all 23 shots he faced in relief.
Jack Eichel scored, and Phil Kessel had an assist for Vegas. Logan Thompson stopped all nine shots he faced in 30:13, and Adin Hill made seven saves in relief.
Eichel gave the Golden Knights a 1-0 lead at 7:10 of the first.
