Bertens, who was a doubles finalist previous year in Singapore, snapped a run of service breaks with a vital hold from 0-40 in the eighth game of the final set before a forehand victor earned the world No 9 a tour-leading 11th victory over a top 10 player this season.
Stephens also hit 16 fewer unforced errors than her opponent during the 2hr 24min match, during which the crowd held up signs in English and Japanese to cheer Osaka on.
"I thought I played a really good match", Stephens said in her post-match press conference.
With the duo's battle taking almost two-and-a-half hours, the second match of the night started at around 10.30pm, and it was another three-set, two-hour-plus battle before Kiki Bertens - a first-time singles participant and a last-minute replacement for the injured Simona Halep - stunned top-seeded Angelique Kerber 1-6, 6-3, 6-4.
Kerber made the fast start in the Red Group meeting as she secured back-to-back breaks of serve before sealing the first set on her third opportunity.
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But the deciding set was one-way traffic as Stephens' greater consistency saw her break Osaka, who made 46 unforced errors in total, three further times to clinch victory.
Pliskova's coach Rennae Stubbs urged her to "stay disciplined" in the next changeover and the Czech heeded the advice to curb her attacking instincts as she ended Kvitova's tournament by holding serve to take the opener in 41 minutes.
"I just competed really well and never gave up", said Stephens.
Bertens capitalised on a rapid drop in intensity from Stephens to reel off four games in a row on her way to taking the second set.
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The Dutchwoman only made it to Singapore when Romanian world number one Simona Halep withdrew through injury but she showed incredible grit and tenacity after falling a set and 2-0 down to fight back for her 11th win over a top-10 player this season.
"I'm playing against the best players in the world, so I feel like I want to be in top form, but I'm not really there".
After trading early breaks, the match settled down as the pair enjoyed more success on serve.
The break was enough for Kerber to seal a brilliant win, with Osaka crushing a backhand into the net on the German's first match point. "But I don't really have any regrets, this entire match was a really hard battle".
"We played a really tough and competitive match so its always an honor to share the court with somebody that good", Stephens added.
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