Porte, who lost 51 seconds in the opening stage after being delayed behind a pile-up, helped his team edge out Team Sky by four seconds after they completed the 35.5 kilometre circuit around Cholet in 38 minutes 46 seconds.
"We're just ... trying to get through the best we can until we get to the mountains", Froome said.
Team Sky, another unusual early starter, were booed by roadside spectators throughout their effort but posted nearly identical times through the first two time checks - as did BMC Racing, who also found themselves in an unfamiliar early start time.
Froome's Sky team mate Geraint Thomas could however prove a thorn in his side as the Welshman, who underlined his credentials by winning the Criterium du Dauphine last month, is third overall, 52 seconds ahead of his leader.
"We expected some crashes in this tricky final and moved up early", said Enrico Poitschke, sports director of Sagan's Bora-Hansgrohe team.
Ireland's Dan Martin also struggled after his UAE Team Emirates finished 15th on the stage, one minute and 38 seconds behind BMC. He also wore the yellow jersey in three stages at the Tour de France two years ago.
Wrong! The Tour de France's stage 3 TTT was an important part of the battle for the yellow jersey. It would have been nice not to have thrown 51 seconds away on the first day.
Among the top contenders, last year's runner-up Rigoberto Uran of Colombia is 10th, 35 seconds behind. Through the jury's decision, in the final version as many as 116 riders had the same time as the leg victor, Peter Sagan (4:06:37 hour) i.e.all those who were in the peloton at the time of the crash.
Thomas, who wore yellow for four days past year, said that he was not bothered by the...
There was no surprises for Movistar's Quintana, who lost another chunk of time to Froome, to whom he came second on the Tour twice.
It was also a very satisfying day for Froome, the Kenyan-born Briton ignoring some booing at the start line and making up some of the valuable time he lost on Saturday's first stage.
The Tour heads into the cycling hotbed of Brittany on Tuesday for Stage 4, a mostly flat 195-kilometer leg from La Baule to Sarzeau that starts and ends on the Atlantic coast.
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