By finishing second in the 35.5km team time-trial around Cholet, Team Sky did that with typical efficiency.
The result saw Bevin's BMC Racing team-mate Greg Van Avermaet take the yellow jersey, while the team's designated leader Richie Porte, who lost 51 seconds on the opening stage, is now up to 14th on the general classification.
Boulder's Taylor Phinney, on the other hand, finished 19 in the stage, just a second behind Froome. I think there will be a lot more time lost throughout the GC group before we hit the mountains.
Van Avermaet's teammate Tejay van Garderen finished on the same time to take second place overall with Sky's Geraint Thomas in third.
"I don't think it is a bad thing to have the yellow jersey for a team looking for a sponsor", said Porte, who crashed out of last year's Tour and lost time in Stage 1 of this edition.
Team Sky (38:50) were second fastest to help four-time victor Froome climb the standings, with Quick-Step Floors another three seconds adrift in third. "We gave it everything we had and it all went pretty much to plan".
"It's amusing because at the end of the day it's just another bike race".
Yates and Froome sit in 81st and 84th places respectively, 67 seconds off yellow but more concerned about the 51 second gap to the likes of Bardet (AG2R La Mondiale), Vincenzo Nibali (Bahrain-Merida) and Mikel Landa (Movistar).
The Tour heads into the cycling hotbed of Brittany on Tuesday for Stage 4, a mostly flat 195-kilometer (121-mile) leg from La Baule to Sarzeau that starts and ends on the Atlantic coast.
"Our aim was to take the maximum time out of all our rivals", he insisted.
"Team EF-Drapac managed to cut their losses for Rigoberto Uran - their powerful TTT team stopping the clock in 39'21" - while Team Sunweb also ensured they lost very little over the potentially tricky parcours.
"It puts us right back in the game". Without the leak we wouldn't even know about it, but that's the nature of sport now.
Thomas, who is set to sign a new three-year deal with Sky, said the prospect of wearing yellow had not been on his mind before the stage, and the bigger disappointment was missing out on a good chance to claim Sky's first team time trial stage in a Tour. "It's been a great little journey over the past couple of months to come to this team and become part of a really tight team time trial unit and to really add to that is something I will be proud of for a long time", he said. "It just shows that we are here, too, and let's get it on". It was a good test for us and the team. "To win the stage with a team like we have here, and especially with the passing of Andy Rihs, is special", Porte said.
Overnight leader Fernando Gaviria came down in a mass high speed crash just 1.3km from the line, which Sagan and around 15 other riders avoided to set up a frantic finish.
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