Both of her first-set leads were conceded immediately, and closing out the first set proved to be something of a struggle.
Ash Barty will need to overcome injury after hurting her arm in her quarter-final win.
Pavlyuchenkova, the world No.39, ended fifth-seed Kvitova's hopes of claiming a third title at Wuhan in five years with a 3-6, 6-3, 6-3 victory. "It was nice to be able to take a couple of my opportunities in the third", said Barty, a finalist here in 2017.
Kerber then held break points on Barty's serve but couldn't capitalise and the 16th seed made her pay with an immediate break to take the first set. "She's one of the best players in the world, and you have to come out here, enjoy and have fun, and try and play as well as you can", Barty said on-court after the match.
Wozniacki won the first three games of the match but failed to build on that strong start, losing the first set after seeing three set points come in go in a long tie-break.
Barty lost in last year's final to France's Caroline Garcia, reports Efe news.More news: Men: Dark Phoenix Trailer Hits
Barty, who won her first tour-level tournament this year in Nottingham, has been in fine form in Wuhan after beating Jo Konta and Zheng Saisai in the first two rounds.
"She's always very hard to play against".
Puig had come from a bagel set down to defeat the Australian Open champion 0-6 6-4 6-4 in the second round at the Miami Open in March and the 24-year-old repeated the dose with a forehand victor to set up a clash against home favourite Wang Qiang, who defeated Daria Gavrilova in straight sets, in an all-unseeded battle.
Also, seventh-seeded Joao Sousa defeated Vasek Pospisil 6-7 (4), 6-4, 7-6 (0), and Bernard Tomic beat Lloyd Harris 7-6 (5), 2-6, 7-6 (6). On Wednesday it was the turn of Puig to send more shock waves through the field of the Wuhan Open as she knocked-out the world number two, Wozniacki.
She will now face Wang Qiang of China, who ousted Australia's Daria Gavrilova 7-5, 6-2 to the delight of the home crowd.