The second seed from the United States fought back in Beijing to beat Veronika Kudermetova 6-7(9), 6-1, 6-2.
The first set was a mammoth one, the 39th-ranked Russian prevailing in the tiebreak to take an early lead.
Pegula struck back in the second set, then carried that momentum into the deciding set and grabbed an early break to give her a sniff of victory.
Pegula, who is chasing a seventh WTA Tour title, sealed the deal with her third match point when she sent down an ace.
The 19th-ranked Badosa booked her place in the next round with a straight-sets win over Slovakian qualifier Rebecca Sramkova.
The top seed in Beijing is Aryna Sabalenka, who defeated Pegula 7-5, 7-5 in New York earlier this month for her third Grand Slam crown.
World number one Iga Swiatek is not in Beijing because of "personal matters".
