Britain’s defending champion had lost 51 seconds to some of his main rivals after a crash in the opening stage but his team’s efforts against the clock around Cholet put him back in contention.
BMC clocked 38 minutes 46 seconds as their Belgian rider Greg van Avermaet took the overall leader’s yellow jersey, with Sky in second place four seconds behind.
“It’s a dream. We rode a good time trial and the whole team worked hard,” said Van Avermaet. “We’ve got some specialists in the team, I’m so happy we got this collective victory.” Overall, Froome is in 18th place, 55 seconds off the pace and still 44 behind 2017 Giro d’Italia winner Dutchman Tom Dumoulin, who with Team Sunweb only lost seven seconds to the Briton on Monday.
Among the top contenders, last year’s runner-up Rigoberto Uran of Colombia is 10th, 35 seconds behind.
Froome’s Sky team mate Geraint Thomas could however prove a thorn in his side as the Welshman, who underlined his credentials by winning the Criterium du Dauphine last month, is third overall, 52 seconds ahead of his leader.
It was all about the team for Thomas, though, even if he missed out on the yellow jersey by three seconds.
“A bit disappointed not to win but it was a technical race because of the wind, changes of direction, up and down as well. We did well as a team but disappointed not to take the win, we were so close,” he said.
“To be honest I didn’t even think about it (the yellow jersey), it was just about winning the stage. Close but not quite quick enough.”
Among Froome’s main rivals, France’s Romain Bardet lost 1:15 on Monday and now trails the Briton by 20 seconds.
Movistar lost 53 seconds, which leaves Colombian Nairo Quintana, twice runner-up, 1:13 behind Froome – a massive amount of time after only three days of racing.
Tuesday’s fourth stage is a 195-km flat ride from La Baule to Sarzeau.