BMC's Richie Porte is level with Froome with their respective teams looking to do well on the team time trial.
The result means BMC's Greg van Avermaet has taken the yellow jersey from Peter Sagan, whose team Bora-hansgrohe set a time of 39:36 after dropping him.
Australian green jersey contender Michael Matthews of Sunweb sits in ninth spot, 11 seconds behind Van Avermaet.
Chris Froome will also be a relatively happy camper after Team Sky finished second on the stage, just four seconds behind the BMC juggernaut.
Bevin said it was a nervous wait watching Quick-Step Floors complete the course, but once they crossed seven seconds back in 38:53 he knew his team had won. On one hand it was a lot of time to lose, but on the other, they are far from out of the race and sit only a small distance off the likes of Froome, Porte and Yates.
Froome was left 55 seconds behind in the overall standings with another week of nervy rolling stages before hitting the Alps.
Defending champion Chris Froome, who fell into a ditch near the end of Saturday's Stage 1, arrived safely with most of the peloton.
Jakob Fuglsang and Astana actually did a very good job considering they started without one of the best riders against the clock in Luis Leon Sanchez after the Spanish veteran crashed out yesterday.
Van Avermaet also wore the yellow jersey for three days on the 2016 Tour.
Gaviria's compatriot Rigoberto Uran nearly lost time after being caught in a late crash around 5km from the finish, but he was paced back to the main group by his EF Education First-Drapac team to stay 10th, 35 seconds behind Van Avermaet.
Hours before France play Belgium in the soccer World Cup semi-final, two Belgian and two French riders broke away but stood little chance as the pace was controlled by the sprinters' teams on a flat terrain featuring a four-kilometre final strait.
Plagued by suspicions regarding his misuse of asthma-related medicine, the four-time tour victor suffered a start to this morning's Tour that will have undoubtedly pleased many of those fans who had booed Froome and Team Sky earlier this week. "We're on track but there's still so much to go through".
"Today, we just handled business", said Van Garderen, who has twice finished in the top five at the Tour but is riding this edition in a declared supporting role for Porte. "We know that Peter (Sagan) is one of the greatest riders of the peloton and I'm happy to compete against him because he makes everything more hard", he explained. "It just shows that we are here, too, and let's get it on".
The only individual time trial of the race comes in the penultimate stage, over a 31-kilometer route from Saint-Pee-sur-Nivelle to Espelette in the Basque country.