After only eight matches were completed on Friday due to rain, the start of play was again delayed by three hours on Saturday with Pegula and Zhu among the first in action as organisers scrambled to get back on schedule.
Zhu, looking for her first win over a top five ranked opponent, began smartly matching Pegula with an early break.
But the Chinese player was unable to sustain the effort as Pegula broke again to take the opener before charging out to a 3-0 lead in the second.
Zhu would hold serve at 3-1 but after Pegula served to increase her lead headed to the bench during the changeover showing signs of distress and asked for the trainer.
A medical time out was called with a doctor coming on court checking Zhu's blood pressure and heart rate as the Chinese player closed her eyes and pointed to her chest.
Following a brief discussion with the chair umpire the match was called with Pegula coming across to check on her opponent.
Next up for Pegula is Canadian Leylah Fernandez (21) who converted all six of her break chances in a 6-4, 6-2 win over Colombian Emiliana Arango (23).
