The result means that Froome, Porte and Yates were all able to take a chunk of time back after each losing 51 seconds in the dramatic end to stage one on Saturday.
The Slovak cyclist has a six-second lead ahead of Gaviria and is another four seconds ahead of Colbrelli in the general classification.
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 on Monday.
Sagan would have been happy to hold on to it, but the yellow jersey isn't his priority for the Tour, and with the top 59 riders overall separated by just 16 seconds, it was going to take something special from Bora-Hansgrohe to keep him on top.
Death Toll Exceeds 100 After Heavy Rainfall Slams Japan
A man and his wife protect their home from water with sand bags in Saka, Hiroshima prefecture. "I've lived here for 40 years". Local government officials said pumping trucks were being deployed to help restore access to some of the worst-hit areas.
Froome's misfortune is a boost for France's Romain Bardet, seen along with Quintana as the four-time champion's main rival in this year's race, and also for Dutchman Tom Dumoulin, the 2017 Giro d'Italia victor.
It is a measure of just how much success Team Sky have enjoyed at recent Tours de France that when Geraint Thomas missed out on the yellow jersey yesterday by only three seconds he barely shrugged.
"It was a huge challenge for the team, it's been incredible for us", said the 33-year-old Briton who was jeered when his name was announced on the starting ramp.
The stage victory saw BMC Racing move their team leader Richie Porte further up the standings, having lost time in a crash on stage one.
"We rode a decent time trial and even if we still lost a lot of time I'm relieved", said Bardet.
George Clooney injured in scooter accident in Italy
The Hollywood actor collided with a Mercedes auto on Tuesday morning while in Puntaldia, Sardinia, on the way to a TV set. George Clooney is interviewed at the premiere for "Suburbicon" in Los Angeles, California last October.
Froome avoided a repeat of his first stage tumble, the Team Sky leader staying out of trouble as he goes in pursuit of a record-equalling fifth Tour triumph.
And though Sky missed out on victory - and a chance to put Geraint Thomas in the yellow jersey - Froome was able to eradicate the deficit to numerous other contenders. It would have been nice not to have thrown 51 seconds away on the first day.
Movistar lost 53 seconds, which leaves Colombian Nairo Quintana, twice runner-up, 1:13 behind Froome - a massive amount of time after only three days of racing.
"Fernando won yesterday and now I'm the one with the yellow jersey, it's been exciting".
The Tour resumes tomorrow with the 195 km flat stage four that runs between La Baule and Sarzeau.
Trump says Putin meeting may be 'easiest'
But his trip to Brussels may end up being less controversial, said Dan Michaels, the Wall Street Journal Brussels bureau chief. Meanwhile, Mr Trump will be largely kept away from central London.
PSG make world record bid for former Liverpool ace, Coutinho
The pair clashed last season over penalty taking duties and it is believed that the 26-year-old would rather see Cavani leave. PSG remain at the centre of an investigation by UEFA after they spent nearly £400m on Neymar and Kylian Mbappe last summer.
McConnell calls Kavanaugh a ‘superb’ court pick
It may not also be his last, with liberal Justices Ruth Bader Ginsburg 85-years-old and Stephen Breyer turning 80 next month. Brett's mother Martha Gamble served as a Maryland state Circuit Court Judge from 1995 to 2001.
Boris Johnson resigns as British foreign secretary
Davis, for his part, insisted that May's position as prime minister is still safe. "I don't think it's a survival issue at all". The British government says Foreign Secretary Boris Johnson has resigned, amid a widening split in the Cabinet over Brexit .
Real Madrid's Ronaldo signs for Juventus
Cristiano Ronaldo has agreed to move to Juventus after nine years at Real Madrid , the La Liga side have confirmed. In an open letter, Ronaldo thanked the Madrid club and its fans for " nine wonderful years ." .