The top seed was given a second set scare by the Chilean but wrestled back control to emerge as the victor in a 6-2 3-6 6-3 encounter.
The two-time grand slam finalist, having been runner-up at Wimbledon and the US Open this year, will face Yoshihito Nishioka after he saw off Japanese compatriot Taro Daniel in a 6-2 6-4 win.
His victory also ensured his place at the ATP Tour's end-of-year finale in Turin, alongside Spanish duo Rafael Nadal and Carlos Alcaraz.
Cameron Norrie remains on course to set up a potential final in Korea with Ruud after brushing aside Kaichi Uchida with a comfortable 6-2 6-2 victory.
The Briton will face eighth seed Jenson Brooksby after he turned over home favourite Kwon Soon-woo in a 6-3 6-4 result in Seoul.
Brooksby's fellow Americans Mackenzie McDonald and Aleksandar Kovacevic also came through their last-16 encounters to set up a quarter-final clash against each other.