The super team covered the 35 kilometres from Pont-de-Vaux to Louhans-Châteaurenaud in 36 minutes and 33 seconds. Lotto-Soudal took the third step on the podium, finishing 53 seconds behind Sky.
With his team's stage victory, Michal Kwiatkowski moves back into the race lead.
He and three of his teammates make up the top four including Geraint Thomas who heads to the mountains 21 seconds behind the Polish rider.
“I’m so happy that I got no major issue after the crash yesterday," Kwiatkowski said. "If I could have picked up one stage win in the Dauphiné, I’d like it to be the TTT.
"It’s a wonderful feeling to win as a team. We rode a perfect stage, technically and tactically, on the entire course. On paper we had the strongest team, but it’s a different thing to win and I’m very happy we did it.”
BMC's ride was good enough to put Brent Bookwalter in a strong fifth overall position, with Quick-step Floors' Bob Jungels the best of the other GC contenders in 10th.
While Romain Bardet now sits one minute and 52 seconds off the pace, his AG2R-Mondiale team rode a respectable TTT, finishing seventh.
But it wasn't a great day for Vincenzo Nibali's Bahrain-Merida who rode haggardly in the final kilometres losing just over two minutes to the winners, the Italian himself now two minutes and 28 seconds in deficit.
Mitchelton-Scott's fourth place contained Adam Yates's disadvantage somewhat to Kwiatkowski and Thomas, but he'll have to find one minute and 17 seconds out on the road over the final mountainous four stages.
More to come.
The race continues with a hard day out in the mountains including a summit finish. Stage four will be streamed here and broadcast on SBS Viceland from 11:15pm AEST.