BMC put 20 seconds into second placed Sunweb while Quick-Step Floors was third at 27 seconds, the victory placing local Stefan Kung into the race lead after he crossed the finish first.
"It's really special to be the leader of this race," BMC's Kung said. "Thanks to the guys for that because everybody did their job and I was the one chosen to go first over the line.
"It means a lot to me. It's my home. It's where I grew up and it's where I competed in my first cycling race ever 14 years ago so the circle is closing. To wear the yellow jersey in my home race is a dream and I am going to enjoy it for sure."
The win also placed Australian Porte in the prime position among the riders vying for the overall title with Nairo Quintana at 33 seconds and defending champion Simon Spilak at 46.
"That was my first team time trial since 2015 when I was with Team Sky and they were beaten by BMC Racing Team. It was absolutely incredible," Porte said.
"You really have to tip your cap today to Stefan Kung. He was like ten men. He was absolutely flying so, it was very impressive."
"I don't think you are meant to feel good in a race like that. It's been a while since I raced so I don't really know where I am at but I mean it was just fantastic to come to the Tour de Suisse, the home of Andy Rihs [recently deceased team owner], and be able to win the stage. I think we dedicate the win to Andy."
BMC started second to last and was chasing the provisional best time of 20min 38sec set by Sunweb. After 10km the squad was ahead of that benchmark by seven seconds and continued on to stop the clock in 20min 18sec.