Saturday's semi-finals will see Bertens take on White Group victor Elina Svitolina of Ukraine, before Stephens faces big-hitting Czech Karolina Pliskova in the night match of a tournament that has seen the four lowest-ranked players advance.
Stephens staved off seven break points early in the first set and added to the German's frustration by converting the first two she fashioned to pull clear for a 5-2 lead after little could separate the baseliners in the opening exchanges.
"It was just getting worse and worse every time I played", said Osaka.
The trend of this tournament suggested the match would go to three sets, however - 10 matches have gone the distance this week, beating the previous high of six - and it duly did so when Svitolina ran away with the second set.
Svitolina had been a virtual spectator during the fightback but shook off her passive play and concentrated on depth as opposed to direction, taking advantage of mental lapses from Bertens to claim the opener when her opponent double-faulted.
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I thought she played well and it was obviously a tough match from the beginning.
Tennis - Germany's Angelique Kerber says she is looking forward to a vacation with her friends after bowing out of the season-ending WTA Finals in Singapore.
In truth, Stephens wasn't really tested against Kerber and got through the match playing in second or third gear. "I'll take it and I'll take my rest, and I have some more recovery time for tomorrow".
Ukraine's Elina Svitolina reacts during the singles final against Sloane Stephens of the USA. She's a tough match.
"I just really wanted to try because this is the last tournament, and I felt it was really unfair to everyone that came to watch".
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Verstappen controlled the race after taking the lead from the start, with Hamilton slotting into second. On lap 17, Hamilton was fixed on Raikkonen's gearbox, with the Finn struggling on worn tyres.
"I had a bit of an adrenaline dump after I finally won one game - I was really fired up, so I was like 'come on, let's do this".
Sloane Stephens of US reacts during the singles final against Ukraine's Elina Svitolina.
"I was clear with what I had to do on court", she said.
"Unfortunately, this is the past year that Singapore is hosting this incredible tournament".
A left hamstring injury seems to be bothering Osaka, although she wouldn't discuss it during her press conference on Wednesday.
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