The Tour remains in western France for Stage 3 on Monday with a 35.5-kilometre team time trial that starts and finishes in Cholet.
"A team time trial is always a something special when the whole team makes efforts for the same goal", Van Avermaet said.
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.
"I'm only some 20 seconds behind Froome so it's not that much". "I think I am in good condition and I have a good team around me but there are no doubts that this is the most important test of the season for me".
While Sky's top placed rider is Geraint Thomas three seconds off the lead, 2017 Giro victor Dumoulin is just 11 seconds down, but perhaps Bardet is the man with the most to smile about at this stage. "We've got some specialists in the team, I'm so happy we got this collective victory".
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're on track but there's still so much to go through".
"I'll be wearing the yellow jersey probably for only one day, but I'm happy for that".
BMC Racing team in the third stage of the Tour de France. "I love France and the Tour, which is the most handsome race on the planet. That's the nature of the game".
Rigoberto Uran's EF Education First-Drapac team gave up 35 seconds in fifth, Mikel Landa and Nairo Quintana's Movistar 54 seconds in 10th, and Vincenzo Nibali's Bahrain-Merida team 66 seconds in 11th.
The latter's hopes of reclaiming the maillot jaune took an early hit, however, as he lost contact with the back of the Quick-Step train and the team split apart early in the stage.
"We rode out of our skin and super smooth and with the horsepower that we have did a great ride", the Irishman said.
On a short climb at the halfway point in the course, however, the Belgian team was forced to regroup as the pace forced riders - including Gaviria - off the back, costing the handful of seconds that might have put Gilbert in yellow.
"We knew it was OK to lose Luke and Wout", Thomas said. "If they could just go as long as they could and if they didn't feel great then just commit anyway, and that's what they did".
Greg van Avermaet was the virtual leader when Peter Sagan, in the yellow jersey, rolled down the ramp with Bora-hansgrohe and Fernando Gaviria set off with Quick-Step Floors.
While Sky missed out, victory was a boon to Porte - a year to the day after he was hospitalised by the serious crash which ended his 2017 Tour - and the BMC team whose future remains uncertain as they seek a new title sponsor.