Vekic came through 7-6 (9/7), 6-2 to reach the quarter-finals after world number two Gauff claimed she was "getting cheated" in a lengthy argument with the chair umpire over a line call in the sixth game of the second set.
Gauff, who had already surrendered a 5-2 lead in the first set, lost her composure on break point when a ball from Vekic was called out.
However, Gauff then hit the return into the net as the chair umpire was correcting the original call and insisted the call had not hindered the American's shot.
The 20-year-old wept as she pleaded her case but the point and break was awarded to Vekic.
"I have to advocate for myself all the time," said an emotional Gauff.
"I'm getting cheated in this game. You guys are not fair to me."
