Playing her second match in three hot and humid hours, the Wimbledon champion overpowered the hard-hitting Thai in 75 minutes to set up a meeting in the final eight with unseeded Frenchwoman Camille Pin.
The 14-times grand slam winner had to save four break points after hitting six double faults but unleashed a series of stinging groundstrokes to get past Tamarine, who was last year's losing finalist.
Williams had two hours earlier finished off the final games of her rain-suspended first-round match to beat Denmark's Caroline Wozniacki 6-2 6-2.
"I played twice today and although the first match was short, I still had to go through all the mental preparation twice," Williams told reporters.
"Tamarine played well, she went for her shots, she played aggressive. I'm playing well because everyone else is playing well against me."
Williams is chasing the Bangkok title to secure points for one of the eight berths at the $3 million season-ending championships in Madrid.
Her quest was helped by the retirement of top seed Jelena Jankovic with heat illness during her first-round match on Wednesday.
Polish wildcard Urszula Radwanska ended fourth seed Virginie Razzano's hopes of a third straight WTA title with a 7-6 7-5 victory.
SPURNED CHANCES
The Frenchwoman spurned three chances to take the tightly contested first set and allowed the 17-year-old to edge ahead in the second to reach her first WTA quarter-final.
Both players were carrying injuries and struggled towards the end of the three-hour duel, with Razzano hobbling and grimacing as her 543rd-ranked opponent played drop shots to pull her into the net.
Radwanska needed a medical timeout near the end of the match and had her right thigh and left ankle heavily taped up. "It was a really difficult match, three hours, and it was very hot," Radwanska told reporters.
"I'm happy to beat her, she's been playing really well, she made it tough for me."
Razzano was chasing a third straight title after successes in Guangzhou and Tokyo in the last two weeks.
Third-seeded Israeli Shahar Peer progressed to the quarters with a 6-1 6-1 win over Russian Anastasia Rodionova, and China's Yan Zi beat Olga Poutchkova of Russia 3-6 6-1 6-1.