The 2023 US Open champion will face Paula Badosa after the Spaniard ended the fairytale run of China's 595th-ranked Zhang Shuai in straight sets.
Gauff, seeded four, fought back to defeat 115th-ranked Starodubtseva 2-6, 6-2, 6-2 in Beijing.
The 20-year-old American recently parted ways with coach Brad Gilbert as she attempts to regain the form that brought her a first Grand Slam crown last year.
Gauff's serve has become a particular problem and it was so again as she surrendered the first set.
But Gauff recovered her poise to battle back in the second - it was the first set Starodubtseva had dropped in her seventh match at the tournament.
Gauff, who is chasing an eighth singles title, surged into a 3-0 lead in the deciding set on the way to sealing her place in the semi-finals.
In the other quarter-final on the day, former world number two Badosa disappointed the home fans with a 6-1, 7-6(4) defeat of Zhang.
The 35-year-old Zhang, a two-time Grand Slam singles quarter-finalist who has been plagued by injury, arrived in Beijing on a run of 24 defeats in a row.
The painful losing run, stretching more than 600 days, was the second-longest on the WTA Tour in the Open Era, which began in 1968.
But the former top-25 player finally won a match to start her tournament and then rattled off three more victories to improbably reach the last eight.
In front of a near-capacity crowd at the 15,000-seater Diamond Court, Zhang went a double break down in a blur of unforced errors.
She finally held to get on the board for 4-1, but Badosa raced away with the first set in 23 minutes.
The second was closer and they went to a tiebreak.
Badosa, who is looking to win a fifth singles title, sealed the deal on her first match point when Zhang's forehand return drifted wide.
Zhang was the lowest-ranked player ever to reach this stage at the China Open.
Top seed Aryna Sabalenka plays Karolina Muchova on Friday for a place in the last four.
The winner will face Russian teenager Mirra Andreeva or China's Olympic champion Zheng Qinwen.
