Kvitova is the most successful player in Wuhan's short history after winning in 2014 and 2016, but she will have to wait for a third crown after Pavlyuchenkova came from a set down to secure a 3-6 6-3 6-3 win.
Germany s Kerber was downed 7-5, 6-1 by Australia s Barty, a year ago s runner-up in Wuhan. It was nice to be able to take a couple of my opportunities in the third.
Puig trailed in both sets and needed six set points to win the first set.
Barty was beaten by Garcia in the Wuhan final a year ago and the Australian stayed in contention to go one better.
The 34th-ranked Wang was moving gingerly before the final game of the first set, and got some on-court treatment on her legs before play resumed.
"It was tough to play in the beginning because my back was blocked", she said.
'Love Corbyn, hate Brexit': Labour faces Brexit split
The party's finance spokesman, John McDonnell, said any such vote should be on how - not whether - to leave the EU. Starmer has said a referendum to reverse Brexit must be an "option", but Corbyn's position is less clear.
In-form Barty is now ranked 17th in the world, and a strong finish in Wuhan - a WTA Premier 5 tournament with 900 points for the victor - could help her inch up the rankings before the end of the season.
Meanwhile, Bernard Tomic fought off a match point to come through 7-6 (7-5) 2-6 7-6 (8-6) against Lloyd Harris.
Also, Japanese qualifier Yoshihito Nishioka upset sixth-seeded Denis Shapovalov 7-6 (5), 3-6, 7-5, and Albert Ramos-Vinolas beat Viktor Troicki 7-6 (4), 4-6, 7-6 (3).
But it was a short-lived fightback as Barty, Australia s top-ranked player, quickly regained control while Kerber struggled to contain unforced errors.
The 51st-ranked Puig was more than a match for Australian Open champion Wozniacki, who missed an opportunity to narrow the gap at the top after world number one Simona Halep was knocked out on Monday.
The second stanza followed a similar narrative to the first as Wozniacki surged into a 3-0 lead before Puig kicked back into action and stormed home to take the set 7-5 and book a quarterfinal meeting with Wang Qiang.