Pervis, 2014 world champion in the keirin, individual sprint and time trial, was second until the last 250-metre lap when he glided past Maximilian Levy of Germany amid deafening roars.
"A month ago I did not know where I was standing. I had to go through physical and psychological barriers to achieve this," the winner told reporters.
Eddie Dawkins of New Zealand claimed the silver and Azizulhasni Awang of Malaysia took the bronze.
There was more cheer for New Zealand when Pieter Bulling, Regan Cough, Dylan Kennett and Alex Frame beat Olympic champions Britain (Ed Clancy, Steven Burke, Owain Doull, Andrew Tenant) in the men's team pursuit final. Australia took the bronze.
Germany top the medals table ahead of France after Lucas Liss won the scratch race ahead of Spain's Albert Torres and American Bobby Lea.
Annette Edmondson, Ashlee Ankudinoff, Amy Cure and Melissa Hoskins gave Australia their first title of the championships in the women's team pursuit, breaking the world record to hand Britain their first defeat in four years.
Australia clocked 4:13.683 as the British quartet of Katie Archibald, Elinor Barker, Laura Trott and Joanna Rowsell suffered their first defeat since December 2010 in Colombia.
Britain set the old record of 4:16.552 in December 2013 in Mexico.
Russian Anastasiia Voinova beat Australian Anna Meares to claim gold in the women's 500 metres time trial with defending champion Miriam Welte of Germany having to settle for bronze.
(Reporting by Julien Pretot, editing by Tony Jimenez)
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