The late-night thriller at Arthur Ashe Stadium wrapped up at 02.15 on Monday, beating the previous record for a women's match at the year's final Grand Slam by two minutes.
"It's always nice to play in the night session because I'm used to it... It's the first time I've played here in New York at two in the morning. It's unbelievable," said Zheng.
"Thanks to the fans that aren't sleeping tonight, supporting me here."
China's Zheng is bidding to become the fourth woman to win Olympic gold and the US Open title in the same year after Serena Williams (2012), Venus Williams (2000) and Steffi Graf (1988). She will meet second seed Aryna Sabalenka next.
The world number seven, who lost to Sabalenka in the Australian Open final, wrapped up an intense opening set against 24th seed Vekic in an hour after raising her level a few notches in the tiebreak.
Vekic was undeterred and responded with the first break of the match early in the second set, but dropped serve immediately as Zheng heaped the pressure on her opponent with some heavy shots from both flanks.
Zheng's service game briefly deserted her as Vekic broke in the 10th game with a backhand winner to draw level in the match, but the Chinese player got her nose in front in the decider and held her nerve to close out the win.
"She's really tough to play on hard courts, she put a lot of pressure on me," added Zheng, who beat Vekic in straight sets in the Olympic final.
"At Roland Garros I was in control. But today she hit really aggressive. It was tough for me to play against her... It was a really nice victory for me."