Ganna (Ineos Grenadiers) put down an early marker, but even the Italian knew it would all come down to the final riders out on the course, those at the top of the General Classification.
"At the moment I'm happy, obviously. We'll wait for the end when the big riders come," Ganna said at the end of his ride.
Evenepoel's second place sees the defending champion move into third place and gain over one minute on overall leader Sepp Kuss.
Kuss went into today's stage with a 43-second lead over Marc Soler, with Evenepoel in fourth place more than two minutes adrift.
The time trial was always going to see Evenepoel, wearing the rainbow jersey after winning the world road time trial in August, make a claim for the leader's red jersey.
More important than beating Ganna, was taking as much time as possible from Kuss. The American put in a great effort to finish 13th in the stage and hold onto the red jersey.
"Let's say that we have to be happy with the GC gaps I took today, and also coming quite closer to Sepp (Kuss) who did, actually, a super good time trial," Evenepoel said after the race.
Ganna, runner-up to Evenepoel in the world road time trial, and one of the favourites for today's stage, posted an impressive time of 27 minutes and 39 seconds.
Nobody came close to Ganna's time until Primoz Roglic hit the road. The Jumbo-Visma rider moved into second in the stage, 36 seconds down on the Italian, and ended the stage in third place after Evenepoel overtook his time.
Ganna lost out on stage five in a sprint finish to Kaden Groves, but the time trial sees him finally achieve one of his ambitions.
"I'm really happy, to win also here was my dream, my goal, so today I can say I did that," Ganna said once his stage win was confirmed.
Roglic moves up into fourth place having started the day in sixth. Evenepoel is now one minute and nine seconds behind Kuss, with Soler 26 seconds off the leader.
Wednesday's stage eleven is a mostly flat 163.5 kilometre ride with an uphill finish, from Lerma to La Laguna Negra.
