"It was a good sprint, slightly uphill in the end, but I had good legs and a good feeling", said Gaviria, only the second Colombian to wear the yellow jersey after Victor Hugo Pena in 2003.
"I'm only some 20 seconds behind Froome so it's not that much".
For the second day a New Zealand cyclist was on the podium at the Tour de France.
Stage victor Slovakia's Peter Sagan, wearing the overall leader's yellow jersey, celebrates on the podium after the second stage of the Tour de France.
Froome has been cleared of any wrongdoing after testing positive for excessive levels of the anti-asthma drug Salbutamol, but the locals have been jeering and whistling the four-times champion since the teams' presentation on Thursday.
Quick-Step Floors, the second last team to start, were the one remaining serious threat that could deny BMC the stage win, and started like a house on fire - so much so that their ranks split apart, with second placed rider overall Fernando Gaviria among those cut loose.
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.
Nairo Quintana (Movistar) lost almost a minute to his chief rivals, while Vincenzo Nibali, Romain Bardet and Ilnur Zakarin also losing decent chunks of time.
It will come as a relief that all except Quintana were able to gain back that time with the help of their teams.
Sagan has won the sprinters jersey five times and is a strong favourite to claim a sixth in Paris.
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It was all about the team for Thomas, though, even if he missed out on the yellow jersey by three seconds.
Geraint Thomas of Sky was third overall, three seconds behind.
"I feel maybe even better (than last year)", Porte said.
The other members of BMC are Kiwi rider Patrick Bevin, Damiano Caruso, Simon Gerrans, Stefan Kung and Michael Schar. "To win the stage with a team like we have here, and especially with the passing of Andy Rihs, is special", Porte said.
"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.
"Earlier in the year, I thought it might have an effect on him", said Wiggins. "It just shows that we are here, too, and let's get it on".
BMC proved the class of the field, completing the 35.5km circuit around Cholet in a time of 38 minutes 46 seconds, four seconds ahead of Sky, to put Olympic champion Greg Van Avermaet in yellow.
Tonight's fourth stage is a flat, 195km stage in Brittany between La Baule and Sarzeau that is expected to finish in a bunch sprint.
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.