The British squad, last to set out, stopped the clock on the 19.2-kilometre stage from the Vallée de Joux to Jurapac in 21 minutes 19 seconds, narrowly ahead of Australian team Orica-GreenEdge and five seconds quicker than Katusha of Russia.
Sky's Geraint Thomas will wear the leader's yellow jersey on Wednesday's 168.1-kilometre hilly second stage from Apples to Saint-Imier.
The Welsh rider, who won the E3 Harelbeke in Belgium last month, wore Romandie's yellow jersey in 2012 after his victory in the prologue.
"We usually come second by a narrow margin so it was great to get the win today," said Thomas.
"The team time trial is something the team wants to target a bit more," he said.
"We've always been up there but we've never really had much focus on it.
"We're looking to keep improving in that area so it's great to win."
Vincenzo Nibali's Astana finished 16 seconds behind while Nairo Quintana is already trailing by 40 seconds after a disappointing showing from Movistar.
The first team time trial on the Tour de Romandie since 2009 served as an ideal warm up for the peloton ahead of the Tour de France's ninth stage, on July 9th, in Brittany.