Marosi, ranked 799th, took a 4-2 lead in the first set but later was broken while serving for the match at 5-4.
The 44th-ranked Pironkova won the first two points of the tiebreaker but Marosi took the next seven to advance.
"It turned out soon that her forehand is much weaker than her backhand, so I played accordingly and also made some drop-shots she didn't like,'' Marosi said.
The other seeded player on court Thursday was Klara Zakopalova of the Czech Republic, who eased into the quarterfinals by beating Mathilde Johansson of France 6-0, 6-1.
"I was playing a good forehand. It was my best stroke today, so I tried to play it as much as I could,'' the seventh-seeded Zakopalova said.
In Friday's quarterfinals at the Romai Tennis Academy, Zakopalova will face Greta Arn of Hungary, who defeated Zuzana Kucova of Slovakia 6-2, 6-1.
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