Greece's Sakkari secured her place in the semi-finals in Fort Worth, Texas, after cruising past seventh-seeded Aryna Sabalenka of Belarus 6-2, 6-4.
Sakkari's second win of the round robin stage left her on top of the Nancy Richey Group with one match remaining.
Sakkari will qualify in top spot from the group if she beats Jabeur in her final first round game.
Jabeur, who had been beaten by Sabalenka in three sets on Monday, shrugged off that loss with a spirited 1-6, 6-3, 6-3 victory over Jessica Pegula of the United States.
Sabalenka however will pip Jabeur for a semi-final berth if she beats Pegula in her final group game.
Pegula was left ruing her failure to capitalize on a fast start in her loss to Jabeur, a losing finalist at Wimbledon and the US Open this year.
The American roared through the opening set, winning six straight games after dropping the first.
Jabeur responded with an early break for a 2-1 lead in the second before dropping her serve at love.
Jabeur managed to right the ship, breaking twice in a row to force the third set.
The decider was tightly contested, Pegula failing to convert five early break points.
Jabeur finally gained the upper hand with a break for 5-3 and polished off the win after an hour and 41 minutes.
"After the first set, she was playing really well and really fast," Jabeur said.
"The balls were tough, very low. I know she likes to play the balls like that. And I just had to find that click to just change up the rhythm and impose my game."