Wiggins, Ed Clancy, Jon Dibben and Owain Doull rode a controlled race, trailing narrowly throughout before a two-lap turn from the former Tour de France winner moved them ahead of their great rivals in sight of the finish line.
However, Clancy – who made his racing return having suffered a career-threatening back injury last year – was dropped from the train in the final lap, allowing the Australian quartet to claim back the gold.
The Australians posted the third-fastest TP ride of all time, a 3:52.727 to win, with Britain's time of 3:53.856 their best performance since the London 2012 Olympics.
Denmark beat Italy to take third, posting a competitive time of 3:55.936 to claim the bronze by just 1.3 seconds.
Laura Trott raised the noise levels in the Lee Valley Velodrome by winning her first-ever scratch race world title, and the sixth rainbow jersey of her career.
In the non-Olympic event, the 23-year-old bridged across to a small leading group on the final lap of the 10 kilometre race, and kept her speed to beat defending champion Kirsten Wild (Netherlands) and Canadian Stephanie Roorda.
Her victory came hours after she was part of the GB team pursuit squad who produced their worst performance in Worlds history.
The quartet – comprising Trott, Joanna Rowsell Shand, Elinor Barker and Ciara Horne – recorded a time of 4:21.454, good enough for fifth.
Winners of the six of the eight world titles previously on offer in the discipline, they will ride against China in tomorrow's first round, and will need to produce at least the second quickest time from what are effectively repechage heats to qualify for the bronze medal final. That is the most they can now salvage from the championships.
Becky James added a bronze medal to Britain's medal tally with a gutsy ride in the Keirin. The Welsh rider, 24, only progressed through the qualifying heats via the repechage, and then pulled a brave move in turn three in the second round to make the final.
Kristina Vogel (Germany) and Anna Meares (Australia) were too strong for her in the final, but the podium place is a welcome result for a rider who has only recently returned to competition after nearly two years on the sidelines through injury.
Nine years after his last sprint world title, Dutchman Theo Bos also returned to the podium in London. The 32-year-old, who rides on the road for Mark Cavendish's Dimension Data team, took silver in Thursday's Kilo. German Joachim Eilers claimed gold with a time of 1:00.042, nearly half a second faster than Bos.
Frenchman Quentin Lafargue won bronze, with Britain's Matt Crampton placing fifth, 0.9 seconds off a medal after producing a PB ride of 1:01.669
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Nick Bull is an NCTJ qualified journalist who has written for a range of titles, as well as being a freelance writer at Beat Media Group, which provides reports for the PA Media wire which is circulated to the likes of the BBC and Eurosport. His work at Cycling Weekly predominantly dealt with professional cycling, and he now holds a role as PR & Digital Manager at SweetSpot Group, which organises the Tour of Britain.