The Pole, ranked fifth in the world, had dropped just six games on her way to the last eight of the WTA International event and appeared set for another straightforward win after taking the first set against her American counterpart.
However, fifth seed Lepchenko displayed superb resolve to fight back and claim a 6-7 (4-7) 6-2 6-2 victory, boosting her hopes of a maiden Tour singles crown.
There was little hint of an upset when Radwanska won an opening set that featured six breaks of serve and then immediately surged 2-0 up in the second.
But Radwanska could not capitalise on that position of dominance as she threw her advantage away before letting an identical lead slip in the decider, Lepchenko winning 26 points off the 2012 Wimbledon finalist's second serve to book her place in the semi-finals.
Lepchenko will now face compatriot Christina McHale after her quarter-final opponent and fourth seed Magdalena Rybarikova retired in the second set with the American leading 6-2 2-0.
Meanwhile, wildcard Maria Kirilenko continued her resurgence by beating sixth seed Kaia Kanepi of Estonia 6-7 (3-7) 6-2 6-3.
Russian Kirilenko, a former world number 10, has dropped to 155 due to a knee injury but once again displayed her considerable quality to come from behind and progress in an encounter that lasted two hours and 21 minutes.
Kirilenko is to take on second seed Karolina Pliskova for a place in the final of the hard-court tournament in Seoul.
Pliskova got just 38 percent of her first serves in against qualifier Nicole Gibbs of the United States, but it mattered not as she eased to a comfortable 6-3 6-4 triumph.