Shortly after taking silver in the pursuit on Thursday, Irvine clinched his first world title in the 15-km scratch race.
"How is it possible to win two medals in one day? I have no idea. It's unbelievable," the 27-year-old, who was born in Northern Ireland, told reporters.
"I just went 100 percent and it paid off. It's a magnificent moment for me and I just want to enjoy it," he said.
"I've been working hard. There's no track in Ireland so I have to travel a lot, training in Mallorca."
Austria's Andreas Muller was second and Australian Luke Davison third in the race over the 60 laps.
Hepburn sped around a fast wooden track over 4,000 metres in four minutes 16.733 seconds, beating Irvine in the men's final by almost eight seconds to give Australia their third consecutive gold medal in the event.
"It's a special feeling," said the 21-year-old Brisbane native, who won a second gold in two days after leading the Australian quartet to victory in the team pursuit on Wednesday.
"It was important for me to defend my title in this event," he added. "I have the ambition for road racing, but the Olympic gold medal is also a big goal for me so in next few years I'll decide if I want to concentrate on the road or the track."
Hepburn's time, however, was well outside of the world record of 4:10.659, set by fellow Australian Jack Bobridge in Sydney two years ago. Bobridge won the title in 2011.
Switzerland's Stefan Kueng won the bronze, beating another Australian Alexander Morgan in the consolation final.
Hong Kong's Lee Wai Sze claimed her first world title, winning the women's 500 metres time trial in 33.973 seconds.
"I must admit, I was very nervous before the start but I knew I was capable of doing a good result," said Lee, who just missed her own Asian record but edged out experienced German Miriam Welte in the two-lap event. Britain's Rebecca James finished third.
The trio of Laura Trott, Dani King and Elinor Barker brought Britain their first gold in the Belarus capital, the Olympic champions crushing Australia in the women's team pursuit final by nearly two seconds. Trott and King were also on the team in London, with Barker replacing Joanna Rowsell.
"The key was that everyone gave 100 percent," said King.
Canada beat Poland for the bronze.
The German trio of Rene Enders, Stefan Botticher and Maximilian Levy upset the favourites to clinch the men's team sprint title, with New Zealand coming second and France third.
Britain, with Jason Kenny and Philip Hindes - part of the team that won Olympic gold in a world record time in London - came a disappointing sixth behind Australia and Russia.
Newcomer Kian Emadi-Coffin had a tough time replacing six-times Olympic champion Hoy who is still pondering his future in the sport, as the British team finished more than a second outside their world mark.