Sabalenka continued to build off of her summer run, moving past Ash Barty in the semifinals 7-6 (2), 6-4 to reach her biggest final.
The unpredictable nature of this year's Wuhan Open meant that 16th seed Ashleigh Barty was the highest ranked player still in the competition at the quarterfinal stage, and the Australian lived up to her billing, defeating Anastasia Pavlyuchenkova 6-2, 5-7, 6-4.
Barty pulled off one of the upsets of the tournament on Wednesday when she knocked out Wimbledon champion Angelique Kerber in straight sets, not allowing the world number three any momentum.
Puig managed to level the first set 6-all and force a tie break that looked as if it might have gone either way.
"And then there was nothing to lose, when she was leading 5-3 (in the first set), and I started to play well".
"I've really been waiting for our next one".
ASH Barty has an injury battle to wage if she is to capitalise fully on being the only seed left in the $2.7 million WTA Wuhan tournament in China.
"I'm really happy to be competing in China, getting a lot of support from fans", she said after beating Australia's Daria Gavrilova in straight sets to reach the last eight. Well, she's a great player.
"It's been an exciting week, and I was lucky to get out of that match", Barty said on court after the match.
She began the second set even stronger, racing to a 5-0 lead as Germany's Kerber struggled to contain her unforced errors.
After a tight first set, Sabalenka broke serve early in the second and was able to keep Cibulkova at arm's length for the remainder of the match, with five aces helping her cause.
Her exit means the first final of 2018 for the 22-year-old Kontaveit, who will be looking to win her second WTA title after enjoying a breakout season in 2017.