BMC won the 28km team timetrial from Vannes to Plumelec on Sunday but Chris Froome tightened his grip on the leader's yellow jersey.
His Sky team may even have beaten the world team timetrial champions but for Ireland's Nicolas Roche cracking on the final 1.7km, 6.2 percent climb to the finish.
Having started the climb 5sec ahead of BMC, Sky missed out on the win by just 0.6 seconds.
"I was pretty generous again in the second half of the course," said a distraught Roche.
"It's true that G (Geraint Thomas) was really strong and that took me out of my comfort zone. I don't have any words to explain my disappointment."
Froome jumped to the defence of his teammate, though.
"At 0.6 seconds, you can't really cut it too finely there to say where we messed up. The guys gave it everything, everyone was really motivated for this team timetrial," he said.
"In the final we saw Nico Roche struggling a little bit up that final climb but that's the nature of the team timetrial.
"He gave so much earlier on, you definitely can't put it down to him struggling on the final climb.
"We gave it everything and BMC were just better than us."
- Nibali losing out -
Froome still put time into the three other members of the 'fantastic four' favourites with reigning champion Vincenzo Nibali losing out the most of all.
His Astana team finished fifth at 35sec from BMC and the 30-year-old Italian is now 2min 22sec behind Froome in 13th place.
Ahead of Monday's first rest day, it was a second disappointing stage in a row for Nibali, who also lost 10 seconds on Saturday, and the Sicilian must regroup quickly before Tuesday's first mountain stage.
Two-time former winner Alberto Contador's Tinkoff-Saxo were fourth on the stage at 28sec and the Spaniard is now fifth overall at 1min 03sec.
Colombian climber Nairo Quintana's Movistar team finished third but only gave up 4sec by the finish and the 2014 Giro d'Italia winner is up to ninth overall at 1min 59sec.
But many eyes will now be on Tejay Van Garderen, who was second to Froome at last month's Criterium du Dauphine, and sits second overall at 12sec.
"We were aiming for the stage victory, yellow would've been a bonus but I couldn't be happier than I am now," said the 26-year-old.
"Watching on TV as Sky were coming, we were biting our finger nails and when we saw we got it by one second, we were just elated."
The American was fifth in the Tour both last year and in 2012 and may now believe he has what it takes to challenge for the overall victory.
And his BMC team managed their challenge for the stage win perfectly, unlike Astana.
- Pushed too hard -
Desperate to gain back some time on Froome, Nibali pushed too hard on the first uphill section inside 10km and shed two of his teammates as Dmitriy Gruzdev and Rein Taaramae lost touch.
Once they hit the final climb to the finish, Nibali led his four remaining teammates all the way, seemingly not even needing to get out of second gear himself.
While Astana's time was perhaps disappointing, at least the Sicilian demonstrated his form is back after his little blip on Saturday's finish up the Mur (wall) de Bretagne.
Movistar suffered similar problems to Astana shortly after the 20.5km second timecheck as Quintana accelerated on a climb and cracked his entire team.
The diminutive climber practically had to stop to wait for them to catch up but they soon regained their shape.
They took the best time at the finish but BMC and SKy kept bettering their times at each check-point, while Tinkoff steadily lost time.
BY the time Sky, running last, reached the final climb it was clear it was a shoot-out between them and BMC, and the British squad had that 5sec lead.
BMC, though, finished stronger and as Roche cracked, the Swiss outfit could breathe a huge sigh of relief.
Source: AFP
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