Tseng was beaten 3&2 by world number 49 Candie Kung, the lowest ranked player left in the draw, before the Taiwanese player then went on to beat Paraguay’s Julieta Granada 2&1 to reach the semi-finals.
Kung will next face world number 37 Vicky Hurst in the semi-finals at the Hamilton Farm Golf Club after the American dispatched reigning US Women’s Open champion Ryu, the current world number 13.
Ryu held the lead on three times against Hurst but could not maintain her advantage as the American levelled up on all three occasions before going ahead herself with a par at the 15th.
Hurst went on to birdie the 16th to go two-up before Ryu bounced back with a birdie of her own on the 17th. But a par from the American on the final hole saw her secure victory in the only last-four match that required the full 18 holes.
Kung raced out to a lead against Tseng in the third round, going 3-up after just seven holes. The world number one stormed back into contention taking back-to-back holes before Kung again fashioned a lead for herself with a birdie at the 10th. Tseng again applied the pressure by taking the 13th but Kung held firm and birdied 15 and 16 to secure victory.
"I wasn't surprised. I lost because I played bad this week," Tseng said. "But it's disappointing. I like match play but I just couldn't get it in the hole."
Kung, fresh from her confidence-boosting win over Tseng, then took the lead on three separate occasions against Granada only to be pegged back each time within two holes.
But the Taiwanese star secured back-to-back birdies on the 15th and 16th before sealing victory with a par on the 17th, Granada also only managing a par on the penultimate hole.
Sunday’s other semi-final will see American Morgan Pressel take on Spaniard Azahara Munoz.
Pressel, seeking her first LPGA win in more than four years, was forced to work hard in her third round clash with Choi, eventually defeating the South Korean in 19 holes, before going on to ease past Sweden’s Anna Nordqvist 5&4.
World number 15 Pressel was on the brink of elimination against Choi when she trailed by two shots with three to play, but found back-to-back birdies on the 16th and 17th to level up before snatching victory on the first extra hole.
"She gave me a tough match," Pressel said. "I made too many mistakes on the front nine, which is why I was down. I made some really big putts on 16 and 17 and I was able to take it all the way."
The American, who made history when she became the LPGA’s youngest Major winner with victory at the 2007 Kraft Nabisco as an 18-year-old, had an easier time of it against Nordqvist, taking the lead on just the third hole and holding on until the 14th when she wrapped up the win with a par.
Munoz booked her place in the last four by first taking out England’s Jodi Ewart 2&1 before going on to beat American Stacy Lewis 5&4 in the quarters.
The 19th-ranked Spaniard eagled the par-5 second to go ahead against Lewis before taking advantage of bogeys by the American on the third, seventh and ninth holds.
Munoz landed a birdie at the 11th to go 5-up before Lewis finally won a hole with a birdie at the 12th. But the Spaniard quickly recovered with a par at 13 before halving the 14th to progress.
Earlier, Hurst had defeated fellow American Angela Stanford 2&1 to reach the last eight while Granada beat Karine Icher by one shot at the same stage. Nordqvist knocked out South Korean Amy Yang 3&1 also in the third round as Ryu defeated Australian Katherine Hull 5&4 and Lewis beat another South Korean, Sun Young Yoo, by two shots.