De Minaur had looked in the mood to race to victory so quickly against an opponent struggling with double-fault trouble — Munar coughed up nine in total — that he would be able to finish before his girlfriend, British number one Katie Boulter, started her all-British election day special against Harriet Dart.
"I might have made it for the start if I hadn't got broken in the last set," he told the crowd afterwards.
"But I'll shower, cool down and do my best to get over there to support Katie.
"This is always the surface I've enjoyed playing on, it's special to play at Wimbledon and hopefully I can go deep into the tournament now."
For all the latest on and off court, join Catherine Murphy, John Millman and John Alexander for the ABC Tennis Podcast on ABC listen.
Fellow Australian Alexei Popyrin secured a memorable five-set victory over Argentinian 30th seed Tomas Martin Etcheverry.
Popyrin, who is ranked 47th in the world, won 3-6, 6-4, 4-6, 6-4, 6-3 to secure a third-round match-up with seven-time winner Novak Djokovic.
Djokovic, who seems to have recovered from a knee injury that forced him to retire from the French Open, defeated British wildcard Jacob Fearnley in four sets.
The news was not so good on the women's side, as Saville's loss to Kostyuk left Australia without a woman in the singles draw, but she did not go down without a fight.
Saville spent three hours and 10 minutes on court against her Ukrainian opponent before ultimately going down 4-6, 7-6(7/2), 6-4.
Australia's world number 82 looked on track for her first third round at the grasscourt major since 2018 after taking the first set and leading 3-0 and 5-2 in the second set.
But Kostyuk, a quarterfinalist at this year's Australian Open, battled back and forced a tie-break with a 20-minute game in the second set that contained seven deuces on Saville's serve.
We acknowledge Aboriginal and Torres Strait Islander s as the First Australians and Traditional Custodians of the lands where we live, learn, and work.
This service may include material from Agence France-Presse (AFP), APTN, , AAP, CNN and the BBC World Service which is copyright and cannot be reproduced.
