In a much-anticipated clash, the 25-year-old Evenepoel made light work of dealing with the four-time Tour de France winner, passing him on the course as he covered the 40.6km in 49:46.03.
Slovenia’s Pogacar, who celebrated his 27th birthday on Sunday, had set out to do the time trial and road race double at the world championship, being hosted over the next seven days in Rwanda, but finished fourth.
Instead, it was Australian Jeremy Vine who took the silver medal in 51:00.83, with Belgium’s Ilan de Wilder in third place in 52:22.10.
It was a statement victory for Evenepoel with his dramatic overtaking of Pogacar two kilometres from the end on the cobbles of Cote de Kimihurura, a 1.3km climb, which made for a difficult finish.
He already had a 45-second advantage over Pogacar at the first time check after 10.6km, and by the third time, after 31.6km, had stretched his advantage to almost 90 seconds as Pogacar’s ambitions faded.
“The first climb was quite hard, together with the last two, but I really pushed it there and after that saw I had quite a big gap, so I just wanted to keep a pace that I could hold until I went flat out on the last climb," Evenepoel said.
"But I'm going to say the cobbles were really… I hated them at some point. It was so hard to really push through them at the end, but to win is the most important."
Vine built on his performance at the Vuelta a Espana, which finished last week and where he won two stages, and was stronger over the second part of the course in Kigali.
Van Wilder’s bronze medal achievement was heightened by the fact that he was making a debut in the time trial at the World Championships.
Pogacar now has a week to prepare for his bid for road race success on Sunday, when the championships are concluded.
Reusser wins women’s time trial
Earlier, Switzerland’s Marlen Reusser won the women’s individual time trial, finishing 51.89 seconds quicker than the rest of the field for a dominant victory.
Reusser took the rainbow jersey in a time of 43:09.34 around a 31.2km course, with Anna van der Breggen from the Netherlands finishing runners-up for a fifth time in 44:01.23, with bronze going to her compatriot Demi Vollering in 44:14.07.