Konta, seeded 11th, beat the seventh seed 7-5 7-6 (8-6) to reach the quarter-finals for the second time.
She also closed the gap on Suarez Navarro in the Race to Singapore, with the Spaniard in the eighth and final qualifying place, two ahead of Konta.
The Briton will play Czech 14th seed Petra Kvitova in the last eight.
Kvitova knocked out world number one Angelique Kerber 6-7 (10-12) 7-5 6-4 in an epic contest that lasted three hours and 19 minutes.
American Madison Keys, currently ninth in the WTA Finals standings, is through to the last eight along with fourth seed Simona Halep, and ninth seed Svetlana Kuznetsova, who beat Venus Williams 6-2 6-2.
Konta held her nerve in a tight contest to overcome Suarez Navarro, edging the first set with the only break of serve and seeing off six set points as she fought back to take the second.
"I was fully prepared to obviously play a third if need be," said Konta.
"I really just tried to be brave and just play the way I wanted to play throughout the whole match, and those points as well."
The Eastbourne-based 26-year-old made the running in the early stages but could not make the breakthrough until the 12th game when Suarez Navarro netted a backhand to give up the set.
The Spaniard grew stronger in the second, twice going a break up and moving 5-3 ahead, but she was unable to capitalise.
Konta played superbly under pressure, saving three set points as she clung on in a game of eight deuces, and then recovering from 6-3 down in the tie-break.
Konta held her nerve in a tight contest to overcome Suarez Navarro, edging the first set with the only break of serve and seeing off six set points as she fought back to take the second.
"I was fully prepared to obviously play a third if need be," said Konta.
"I really just tried to be brave and just play the way I wanted to play throughout the whole match, and those points as well."
The Eastbourne-based 26-year-old made the running in the early stages but could not make the breakthrough until the 12th game when Suarez Navarro netted a backhand to give up the set.
The Spaniard grew stronger in the second, twice going a break up and moving 5-3 ahead, but she was unable to capitalise.
Konta played superbly under pressure, saving three set points as she clung on in a game of eight deuces, and then recovering from 6-3 down in the tie-break.
