The Manchester United midfielder and Ivanovic have been dating since early last year, and the 2008 French Open champion recently relocated to England to be closer to her football beau.
Meanwhile, the victory capped an amazing few days for the 25-year-old Broady, who arrived in Auckland late last week to sign in as a qualifier. Due to the extensive rain delays on Saturday she didn't take the court until almost 11pm for her first qualifying match, which was played indoors with no spectators.
"There were three people watching - my coach, her coach and a friend," laughed Broady. "Then you come out here a few days later and you are playing in front of a full stadium against the number two seed. It's not sunk in yet... I was quite emotional in the last game so I was pleased I managed to hold it together.
Broady looked the more confident player from the beginning of the match, against the notoriously nervy Ivanovic. The Serbian started to find her range as the match progressed but struggled against Broady's power and pace from the service line, as the Brit sent down 14 aces.
"I felt Naomi was using the angles really well and it was hard to read her serve, there were no patterns," said Ivanovic. "It was very tough, I don't remember the last time I was aced that many times."
Broady, who practises at the same facility in Bolton as the Serbian star, said belief was the key to the surprise result.
"My coach said before the match the biggest thing would be believing you could win," said Broady.
"The fact that the young girl went out before me and beat Venus [Williams] gave me a boost - if she could take out Venus, why couldn't I take out the number two seed?"
Broady faces highly rated Latvian teenager Jelena Ostapenko in the second round.