Suarez Navarro next faces twice Rome champion Maria Sharapova who downed Russian qualifier Daria Gavrilova 7-5 6-3.
Sharapova had to work extremely hard to defeat fellow Russian Gavrilova who left the court after the 11th game for treatment to an abdominal muscle injury and was clearly hampered on her return.
"She was obviously affected by it when serving," Sharapova said. "But once you got into the rallies she moved and defended very well."
Suarez Navarro, who leads the tour this year in wins with 31, won the opening two games but once Halep settled down she started to dominate the rallies with her precise ground strokes.
"It was such a tough match from a physical standpoint," Suarez Navarro told SuperTennis TV. "The biggest improvement I've made this year is in my mind."
The Romanian reeled off six straight games to take the opening set.
An easy miss off of a bounced overhead in the third game of the following set seemed to rattle Halep's confidence as she became more tentative, especially on her forehand.
Suarez Navarro took advantage to take the lead as Halep's frustration became clearly visible after she cracked her racket in distress in the sixth game.
With more time to hit, the Spaniard forced a decider repeatedly running Halep around the court with her breath-taking one-handed backhand.
Neither player could hold serve in the first eight games of the decider before Halep led to lead 5-4.
Resiient Suarez Navarro then got her service game together and after breaking again to lead 6-5, finally got over the line with her third match point.
source:eurosport