Liu, who shared the overnight lead with world number one Park Sung-hyun, was four-under over her last four holes -- with an eagle at the par-five 15th and back-to-back birdies to finish -- to overtake Spain's Ciganda with a 54-hole total of 19-under 197 at the Wildfire Golf Club in Phoenix, Arizona.
Ciganda had roared up the leaderboard with a blemish-free nine-under par 63 -- playing her last five holes in five-under with a birdie at 14 followed by an eagle at 15 and birdies at 16 and 18 -- where she rolled in a 15-footer to take the lead.
"I'm not very comfortable and not very used to playing in the last group," admitted 23-year-old Liu said. "I've had two experiences before and I didn't do very well. Today was definitely a turnaround."
Ciganda, meanwhile, was just enjoying watching the birdies land in her impressive round.
"It's a lot of fun," Ciganda said. "When you make putts, it's great. Really I've been playing great. I'm hitting lots of greens so it was a matter of making lots of putts."
Nine-under to start the day, the Spaniard had four birdies on the front nine, but she was fighting to stay patient as she opened the back nine with four straight pars.
At the par-three 14th, she said, "I hit a really good shot there, tap in.
"They put the tee up on 15 so I hit driver, seven-iron, made a good putt for eagle."
Birdies followed at 16 and 18, putting her alone in front until Liu powered past her to put herself in prime position to join Feng Shanshan as the only Chinese players to win on the LPGA Tour.
It was a further two strokes back to American Angel Yin, who carded a 66 for 200.
Park fired a 69 to head a group on 201 that also included former world number one Lydia Ko of New Zealand, who posted a 67.
South Koreans Kim Hyo-Joo and Ko Jin-young both carded 64s to join the group sharing fourth along with Nelly Korda, who carded a 66.
Spain's Azahara Munoz showed early on that low scores were possible, firing a bogey-free 63 that like Ciganda's included seven birdies and an eagle at 15.
Munoz grabbed her eagle despite chunking her approach. She pitched in from some 70 yards out.
"It was fun today," she said. "Everything was working."