"We are all really happy – it's a really special moment," Roglic said.
"Getting the jersey was not really a big objective – we just wanted to do a nice team time trial. But as we managed to take it, we will try and defend the jersey in the next days.
"There was quite a lot of communication out on the road because it was a really hard climb. I think all the guys did a really good job, each and every one of them. It’s a really nice win."
New Zealand's Patrick Bevin lost the leader's green jersey after a disappointing performance from BMC Racing squad as they finished sixth and 38 seconds behind.
Roglic leads Quick-Step Floors duo Julian Alaphilippe and Bob Jungels by six and 16 seconds respectively, with Bevin slipping down to fourth.
Team Sky finished the time trial fourth, leaving Dutch rider Wout Poels fifth overall.
(Reporting by Hardik Vyas in Bengaluru, editing by Ed Osmond)
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