"I don't think it is a bad thing to have the yellow jersey for a team looking for a sponsor", said Porte, who crashed out of last year's Tour and lost time in Stage 1 of this edition.
Chris Froome's pursuit of a record-tying fifth Tour de France title has begun amid big crowds under sunny skies on an island off the Atlantic coast.
The result saw Bevin's BMC Racing team-mate Greg Van Avermaet take the yellow jersey, while the team's designated leader Richie Porte, who lost 51 seconds on the opening stage, is now up to 14th on the general classification.
The Slovak was thrown out after the fourth stage 12 months ago for sending Mark Cavendish crashing in a chaotic sprint, but he won it clean this time to beat Italian Sonny Colbrelli and France's Arnaud Demare into second and third places.
BMC Racing were four seconds quicker than their nearest rivals, Team Sky, in the stage three team time trial.
The three-time defending world champion took the overall lead of the Tour on Sunday after he bettered about a dozen other sprinters to win Stage 2.
The Briton crossed the line 51 seconds behind Tour debutant Gaviria, who won a bunch sprint after the 201km ride from Noirmoutier-en-l'Ile ahead of world champion Peter Sagan and German Marcel Kittel, second and third respectively.
"It's a dream. We rode a good time trial and the whole team worked hard", said Van Avermaet.
Nairo Quintana (Movistar) lost almost a minute to his chief rivals, while Vincenzo Nibali, Romain Bardet and Ilnur Zakarin also losing decent chunks of time. "When you are arrogant, one day or another, there is always something that brings you back to humility".
Froome is aiming to join Jacques Anquetil, Eddy Merckx, Bernard Hinault and Miguel Indurain as the only riders to win the Tour five times. It also put American teammate Tejay van Garderen in second place at the same time.
Geraint Thomas of Sky was third overall, three seconds behind.
Overall, Froome is in 18th place, 55 seconds off the pace and still 44 behind 2017 Giro d'Italia victor Dutchman Tom Dumoulin, who with Team Sunweb only lost seven seconds to the Briton today. Me and Mikel [Nieve] sat on for the first part where it was fast, and then towards the end we started pulling a couple of turns to give the boys a bit of recovery.
The other members of BMC are Kiwi rider Patrick Bevin, Damiano Caruso, Simon Gerrans, Stefan Kung and Michael Schar.
"I feel maybe even better (than last year)", Porte said.
Quick Step Floors had gone out onto the course with the opportunity of getting Fernando Gaviria back into the overall lead, and also had a chance of getting Philippe Gilbert into the yellow jersey should the Colombian be tailed off. "Nothing is going to change, we just have to try to stay out of trouble and hope we get lucky".
The only individual time trial of the race comes in the penultimate stage, over a 31-kilometer route from Saint-Pee-sur-Nivelle to Espelette in the Basque country.