The 24-year-old Evenepoel, who won the time trial and road race at this year's Paris Olympics, roared around the 46km course on his stunning golden bike, winning by six seconds.
Former world champion Ganna clawed back some time but Evenepoel had enough in reserve and raised his arms in triumph as he added yet another victory to his resume.
Italy's Edoardo Affini was third, the only other rider within a minute of Evenepoel whose biggest concern was when his chain fell off moments before he started.
"I felt pretty good at the start and then had a bit of a difficult moment on the climb," he said. "It was maybe the most difficult time trial of my life. But in the end we won."
Brown is set to retire after next week's road race but made sure she will leave te sport as a world champion with a stunning performance to claim a rare double.
The 32-year-old became the first rider in history in men and women's racing to take the Olympic and world title in the same year, a feat matched by the mighty Evenepoel shortly afterwards.
Brown was behind Dutch rider Demi Vollering at the second checkpoint on the 29.9km route but staged a remarkable turnaround to claim the title by 17 seconds.
"Honestly it feels like I'm in a dream these last couple of months," she said. "These big goals that seem ambitious but I've been able to get out on the road and realise those dreams so it's been cool.
"I'm still finishing up at the end of this season and I just feel really, really lucky to have the end of my career like this. It's special."
