Valenzuela, chasing a first LPGA title, won the first two holes to grab an early lead, and was three-up after winning the 14th with a par.
But Nordqvist, winner of four Solheim Cup titles with Europe, won the 15th and 16th with a par and a birdie to cut the deficit to 1-down.
Valenzuela chipped in for par to tie the 17th and preserve her advantage and matched Nordqvist's par at the last.
"A little bit of an adrenaline rush definitely towards the end, but really happy with this win," said Valenzuela, who is one of five players who have now won all four of their matches so far this week. "That chip-in on 17 was really huge and gave me a lot of momentum going into the last one to just close the match."
In Saturday afternoon's quarter-finals, Valenzuela will face Sweden's Linn Grant, who beat Ecuador's Daniela Darquea 4&3.
Last year's runner-up, Ayaka Furue of Japan, advanced with a 2&1 victory over Sweden's Maja Stark, lining up a meeting with France's Celine Boutier, a 4&2 winner over American Angel Yin.
In other round of 16 matches, Leona Maguire of Ireland defeated France's Perrine Delacour 5&3 to set a last-eight meeting with American Lindsey Weaver-Wright, who beat Sophia Schubert 4&3.
Thailand's Pajaree Anannarukarn beat Cheyenne Knight 3&2 and will face Spain's Carlota Ciganda, who eliminated Alison Lee 2&1.
