The third-seeded Gauff ended Pliskova's 11-match winning streak on Wednesday (Thursday AEDT).
The 19-year-old American built a 4-2 lead in the second set before a lengthy back-and-forth with chair umpire Pierre Bacchi.
Gauff complained to Bacchi that he called her serve at deuce out, only after Pliskova had returned it into the net.
The American had to repeat her first serve and went on to hold for a 5-2 lead.
The US Open champion said the argument "fuelled" her.
"It's OK. It's just one point. That happens in tennis. Players make mistakes. Everybody makes mistakes," Gauff said in her on-court interview.
"It kind of went upward from there for me."
Gauff will next face Anna Kalinskaya after the Russian beat ninth-seeded Jelena Ostapenko 6-4 7-5.
Top-ranked Iga Swiatek advanced to the last eight by beating two-time Dubai champion Elina Svitolina 6-1 6-4.
Elena Rybakina was made to work hard for her three-set win over Magdalena Frech in Dubai. (AP PHOTO)
Fourth-seeded Elena Rybakina had a tougher time reaching the quarter-finals. She outlasted Magdalena Frech 7-6 (7-5) 3-6 6-4.
Swiatek will next play sixth-seeded Qinwen Zheng, who eliminated Anastasia Potapova 6-3 6-2.
Rybakina has a quarter-final match-up against Jasmine Paolini, after the Italian defeated eighth-seeded Greek Maria Sakkari 6-4 6-2.
The other quarter-final pits seventh-seeded Czech player Marketa Vondrousova against Romania's Sorana Cirstea.
13°C