Zheng, who received a wildcard entry to the tournament after recovering from an elbow injury, became the first Chinese player to reach the final in Beijing as she outplayed Belgian 13th seed Mertens 7-5 6-2 after Andreeva crushed Bartunkova 6-2 6-2.
Olympic champion Zheng made an early break to build a 4-2 lead, but made a number of errors to hand Mertens the break back.
But the 24-year-old, who is chasing her first WTA 1000 title on home soil, remained calm to build a 6-5 lead, before her strong crosscourt forehand earned her another break point which she converted when Mertens netted.
Zheng dominated the second set to secure her second clash with Andreeva, having beaten the Russian when they met in the 2024 Beijing quarter-finals.
"I think for sure in these [last] two years, both of us, we became more mature," Zheng said in her post-match press conference.
"She just won Roland Garros this year. It was a really great achievement for her.
"She's always a tough opponent because she's always there fighting. A very consistent player. I would say it is not an easy match, but I'm also a tough player. Tomorrow is going to be a hard battle."
Meanwhile, fourth seed Andreeva took an hour and 14 minutes to beat Bartunkova and reach her second WTA 1000 final of the year.
Czech Bartunkova committed 20 unforced errors, twice as many as Andreeva, as the world number five hit 27 winners to clinch victory.
"Just tried to play aggressive, I'm really happy with how I was playing. I really tried to be brave no matter what, and super happy with my performance today," Andreeva said.
