Sky finished second and Quick-Step Floors came third, seven seconds behind. World champion Sunweb featuring Tom Dumoulin finished fifth, 11 seconds back.
Former leader Peter Sagan was dropped by his Bora Hansgrohe teammates and fell to 80th overall, three minutes behind.
Van Avermaet, a Belgian who excels at single-day classics, isn't a threat for the overall title but he could keep the lead through the cobblestoned Stage 9 ending in Roubaix.
Froome was left 55 seconds behind in the overall standings with another week of nervy rolling stages before hitting the Alps.
"It's a good time," said Froome, who dropped 51 seconds following a crash in Stage 1 . "There are a lot of other good teams. As I've said from the start, the legs are good. It was a good test for us and the team. I'm very happy with the other riders."
Froome is aiming to join Jacques Anquetil, Eddy Merckx, Bernard Hinault and Miguel Indurain as the only riders to win the Tour five times.
Van Avermaet earned the yellow jersey by leading BMC over the line, just ahead of American teammate Tejay van Garderen, who moved up to second overall, with the same time as Van Avermaet.
Geraint Thomas of Sky was third overall, three seconds behind.
Among the overall favourites, Dumoulin was seventh (11 seconds behind), last year's runner-up Rigoberto Uran was 10th (:35), Porte was 14th (:51), Movistar teammates Alejandro Valverde and Mikel Landa were 17th (:53), Froome was 18th (:55), Adam Yates was 20th (1:00) and 2014 champion Vincenzo Nibali was 22nd (1:06).
Squad leaders traded turns on the front of the team "trains," with the ability to constantly maintain a fast pace the decisive factor over a challenging — if not highly technical — route featuring a few minor hills.
Times were taken from the fourth rider on each eight-man team to cross the line.
BMC, which is searching for a new title sponsor, also won the previous team time trial on the Tour in 2015.
"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.
"I feel maybe even better (than last year)," Porte said. "It wasn't ideal to throw 51 seconds away but we have taken some good time back on some of the other GC (general classification) guys today. It's a long way to go, we still have six more hectic days and then we have also got the Alps and the Pyrenees."
The other members of BMC are Patrick Bevin, Damiano Caruso, Simon Gerrans, Stefan Kung and Michael Schar.
"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.
"Right now it is more about chest-thumping and psychological advantages. It just shows that we are here, too, and let's get it on."
Van Avermaet also wore the yellow jersey for three days on the 2016 Tour.
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.
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.
