Britain's number two Keothavong, ranked 88 in the world, won 6-4 6-1 in an hour and 22 minutes against the tournament's number two seed.
She will now play either Sania Mirza or Japan's Ayumi Morita in the next round.
Fellow Brits Heather Watson and Laura Robson both went out in the first round of the outdoor hard court tournament in Thailand on Tuesday.
Watson also suffered first-round defeats at Hobart and the Australian Open as she searches for a first WTA Tour win this year.
A solitary break gave King the first set and two more in the second set saw her win in one hour and 30 minutes.
Robson retired in the first set against Amanmuradova.
The disappointiment for Watson and Robson comes after Britain beat Austria 2-0 on Saturday to secure a World Group II play-off in April.