Second-seeded del Potro, champion in 2009, beat four-time champion and eight-time semifinalist David Ferrer 6-4, 6-4 in just under two hours Friday while Bautista Agut, the 2016 champion, defeated Robin Haase 6-7 (7), 7-6 (3), 7-6 (5) in a three-hour marathon.
Del Potro's form in Auckland this week has been outstanding and he has shown no signs of a wrist injury which has dogged his career.
"It's never easy against David because he runs a lot and he's a fighter," del Potro said. "You never know what will happen but I took my chances and got through."
Bautista Agut broke Haase in the seventh game of the second set but Haase immediately broke back and the set again went to a tiebreak. Haase slipped up early and couldn't recover.
The third set proceeded more swiftly with a series of rapid service games until Haase dropped serve in the fourth game.
Bautista Agut gained the early advantage and although Haase again fought back, the fifth-seeded Bautista Agut converted his fourth match point with a lob that just nipped the baseline.
"It was a great finish and when I saw that last ball in I went crazy," Bautista Agut said.