BMC edged out Etixx-Quick Step by two seconds on the 22.7km course, finishing with a time of 23min 55sec at an average speed 56.497kph, while FDJ were third at nine seconds.
Oss holds the leader's blue jersey jersey after he crossed the finish line as first rider in the BMC train. He is followed by team-mates Tejay van Garderen and Greg Van Avermaet on the general classification.
"It wasn’t a priority to discuss who’d cross the line first as we were busy putting a winning strategy together," Oss said.
"I represent the team who won today. It’s my first time leading the overall classification of a WorldTour race. It’s a honour, a privilege, a satisfaction.
"The team time trial was our first goal but the main one is the final overall classification with Tejay van Garderen.
"There are also the next two stage finishes that suit Greg van Avermaet really well. He’s in great form and it’ll be a question of having the legs."
Vincenzo Nibali's Astana team finished 6th at 15sec and Movistar (Alejandro Valverde) 10th at 29sec.
The big general classification loser was Rigoberto Uran whose Cannondale team crashed then finished last at more than two minutes in arrears.
The 207km second stage from Camaiore to Pomarance is punctuated with climbs and features an uphill finish.