Watson needed only two sets but almost two hours to overcome France's Pauline Parmentier - ranked two places below her at 73rd in the world.
But Laura Robson, seeded eighth for the tournament, was beaten in a third-set tie-break by Kai-Chen Chang of Chinese Taipei.
Watson's match featured 12 breaks of serve in 21 games, with the Guernsey player grabbing her fourth late in the first set to win it 7-5.
Three more followed for the 20-year-old in the second set as she wrapped up a 7-5 6-3 win.
Robson dropped her serve twice as she lost her first set to the world number 134, but battled back to win the second and level the match.
The third set went with serve all the way, with not even a break point for either player, but Chang took the deciding tie-break to complete a 6-4 3-6 7-6 (7/4) win.
There was another upset as Misaki Doi ensured a Japanese presence in the semi-finals with a 2-6 6-1 6-3 win over seventh seed Chanelle Scheepers of South Africa. Doi will face Watson in the last four.