Pegula dropped her first set of the tournament in a scrappy opener featuring seven service breaks, but she raised her level after that against the 18-year-old.
Serving with more authority and cutting out the unforced errors, she won four games in a row after losing the first game of the second set and did not look back.
Jovic, the 16th seed, began to look dispirited in the third set as the 32-year-old Pegula moved quickly towards the finish.
"That was really tough," Pegula, who has made at least the quarter-final stage of all four Grand Slams, said on a sunny Court One.
"Iva's a great player and brings lots of energy and intensity, and I just couldn't find my serve in the first set even though I wasn't playing badly.
"Luckily, I started to serve better."
Pegula, one of five American women to reach the last 16 for the first time since 2002, could face a compatriot in the last eight if Coco Gauff beats Switzerland's Belinda Bencic later on Sunday.