The 7.4-km ride into the southern resort of Marbella, which included several narrow, sand-covered stretches, will not count towards the overall standings due to safety concerns and Sky were focused on avoiding mishaps and saving energy for Sunday's second stage as the team came home in 20th place out of 22.
BMC Racing of the United States, who also won the team time trial at last month's Tour de France and are the world champions, were first in eight minutes 10 seconds.
Tinkoff-Saxo of Russia and Australian outfit Orica were second and third respectively.
Slovakian rider Peter Velits led BMC over the line and will wear the red leader's jersey on Sunday, a hilly 158.7-km stretch into Caminito del Rey.
"When we’re the world team time trial champs we have to do the stripes proud," rider Tejay van Garderen told reporters. "It’s a tricky course but in the end the guys stepped up and did us proud."
Sky rider Geraint Thomas said it was "a big disappointment" the stage had been neutralised.
"When the organisers said there weren't going to be any times taken ... we decided to take it easy and stay upright," he explained.
"I rode most of the race on my sidebars because it was so bumpy and because there was a lot of gravel and sand on the corners. If everyone had gone flat out it might have been quite dangerous."
Froome, who also won the Tour de France in 2013, was runner-up in last year's Vuelta behind Spaniard Alberto Contador.
Contador is not contesting this year's race, the 70th edition of the event, after winning the 2015 Giro d'Italia but struggling on the Tour.
Frenchmen Jacques Anquetil (1963) and Bernard Hinault (1978) are the only riders to have won the Tour and the Vuelta in the same year.
(Reporting by Iain Rogers, editing by Tony Jimenez)
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