The last team out on the course was the one with the rider in the overall lead, Bora Hansgrohe, and as they approached the second time check it was clear that Peter Sagan would be surrendering the yellow jersey, the road world champion blowing up moments later, putting it beyond doubt that the lead would change hands.
Sky finished second and Quick-Step Floors came third, seven seconds behind.More news: OnePlus 6 256GB Midnight Black now available in India
"It's about what I expected, we thought we'd lose a bit to Froome and we lost a bit to Froome", said the dry-witted Quintana.
Team time trials test the both the strength and emotional harmony of a team, with the rules structured to prevent the strongest riders making a solo charge and forcing each squad to make hard decisions over whether to leave team-mates behind, and there were indications of splits and frustrations in several groups.
Van Avermaet earned the yellow jersey just ahead of American teammate Tejay van Garderen, who moved up to second overall, with the same time as Van Avermaet.
Ireland's Dan Martin also struggled after his UAE Team Emirates finished 15th on the stage, one minute and 38 seconds behind BMC. It would have been nice not to have thrown 51 seconds away on the first day.
Froome avoided a repeat of his first stage tumble, the Team Sky leader staying out of trouble as he goes in pursuit of a record-equalling fifth Tour triumph.More news: One dead in Pretoria charter plane crash
Vincenzo Nibali's Bahrain-Merida squad were 11th on the day, giving up 62 seconds to Team Sky, while Romain Bardet's AG2R La Mondiale team finished 12th, 71 seconds back.
"It was a strong effort from everyone", said the 33-year-old.
Movistar lost 53sec, which leaves Colombian Nairo Quintana, twice runner-up, 1:13 behind Froome - a huge gap after only three days of racing.
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.More news: Trump to be greeted with 'Trump baby' blimp in London
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