Sakkari broke twice for a 5-1 cushion en route to capturing the first set, which meant Tunisian world number two Jabeur had no mathematical chance of advancing even if she had rallied back to victory.
In the second set, with Sakkari and Sabalenka already safely into the knockout stage, the Greek world number five broke early for a 3-1 lead and raced home from there to improve to 3-0 in the stage of the season-ending tournament.
"I'm trusting myself, I'm just fearless on the court and I am enjoying myself here," Sakkari, who has not dropped at set in Fort Worth, said during her on-court interview.
"There is no secret behind how I am playing but I think it was about time just to start playing good again and I am very happy that it's actually happening here."
By winning her group, Sakkari will face either Frenchwoman Caroline Garcia or Russian Daria Kasatkina in the semis while Sabalenka will face world number one Iga Swiatek.
In the day's first match, Belarusian world number seven Sabalenka eliminated Jessica Pegula from the WTA Finals with a 6-3 7-5 victory to improve to 2-1.
Sabalenka made a blistering start, breaking Pegula to open the match and again for a 5-2 lead. World number three Pegula then fought off four set points to break straight back but Sabalenka broke to love in the next game to wrap up the set.
Pegula fell behind 2-0 in the second but fought back before Sabalenka, at 3-3, delivered a love hold and then came back from 40-15 down for a crushing service break before the top-ranked American returned the favour to extend the set.
But Sabalenka held to love for the third time in the set and fourth in the match for a 6-5 lead and then closed it out on her second match point when she ripped a backhand crosscourt winner.
"She's an amazing player and she made me really work tonight," said Sabalenka. "Just happy that I was really focused from the beginning to the end and I was able to finish this match in two sets."
