It was only the sixth time this year Osaka has played in a three-set match but the unforced errors returned in a one-sided final set.
When she failed to capitalize on four break points in the fourth game of the second set, she made a visible shrugging gesture with both hands.
A pair of easy holds and an another break took her to 5-1, and the 2017 U.S. Open victor sealed the contest on her second match point when an anguished Osaka double-faulted for the fourth time in the match.
The American struggled mid-match but fought back from an early break in the third set to prevail 7-6 (7/4), 2-6, 6-3 in two hours and 20 minutes.
Bertens will conclude her Red Group round robin play against American Sloane Stephens and Naomi Osaka of Japan, and the Dutchwoman is hoping she can dictate terms a little better in those matches. She was rewarded with a break and closed out the first set, much to the racquet slinging frustration of Naomi Osaka.
Osaka later acknowledged that her inconsistency was the difference in the match, with Stephens forcing her deep behind the baseline, which was not her usual playing style.
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"I just competed really well and never gave up", Stephens said in a post-match interview. She blinked ever so slightly as Stephens picked off two games on the spin to close the gap, before Osaka levelled things up.
"Obviously playing someone with a lot of confidence is always a tough task, but I think that I played well and I kept a good attitude".
To say it "went a little better" is an understatement with Bertens breaking her German opponent twice to level the contest before she emerged from the topsy-turvy decider with her 11th victory over a top-10 player this season. Osaka got her reward though with a break before deflecting another point on her own serve to go up 5-2.
That hard-fought hold triggered a three-game mini run for the third seed, though the pair exchanged further breaks before Stephens - who often relied on her superb defensive capabilities to launch effective counter strikes against the aggressive Osaka - gifted the set to her opponent by sending down a double fault.
Bertens was the last player to make it into the eight-woman tournament when world number one Simona Halep withdrew through injury. "In the third set I had so many chances and I couldn't take it".
The world number four also felt that her regular displays of emotion in Singapore were a result of not being able to follow through on her burning desire to win matches.