Movistar rider Dowsett looked poised to challenge the time of five minutes 57 seconds set by Trek-Segafredo's Italian rider Fabio Felline, but overshot the final corner and paid the price as he finished two seconds down in second place.
Team Sky's Froome conceded 29 seconds to Felline to finish a lowly 78th but was in the company of several other GC hopefuls who opted not to risk too much on the slippery 4.8km circuit around Aigle.
Their fears were confirmed by the sight of BMC's American rider Tejay van Garderen hitting the deck, although he recovered to finish only five seconds behind Froome, and one second down on team-mate Richie Porte.
Briton Simon Yates of Orica-Scott finished in a time of six minutes 15 seconds to take 25th place, one second and one place behind Irishman Nicolas Roche of BMC, while Lotto NL Jumbo's Primoz Roglic was the best placed of the GC hopefuls, sixth overall and nine seconds down.
"It was really sketchy out there," Froome said on Team Sky's website. "The main thing for me today was to just stay upright. It's not worth coming off on one of these corners at this point in the season. Having said that I'm a good 20 seconds back, most notably on Roglic at the moment, so that's going to be hard to make up.
"But let's see. We've got a week of racing ahead of us. Romandie is one of the key races in my build up to the Tour and hopefully I'll be able to go away with a solid week of racing in my legs by the end of the race."
Read the original article on Eurosport: Chris Froome plays it safe in prologue as Alex Dowsett denied stage win