The 2013 Tour winner Froome almost caught Rodriguez near the top of the day's final climb, but the Spaniard held on for his second career Tour stage win five years after his first.
"I didn't expect to be in yellow this early on. Couldn't be a better feeling," said Froome, whose title defense ended when he crashed early in last year's race. "I may look calm on the outside but I assure you I'm not. A huge thank you to my teammates, they turned themselves inside out to keep me at the front."
He now leads German rider
More importantly, Froome's touted main rivals are lagging.
Froome is now 36 seconds clear of two-time champion
“I'd rather be in this position that I'm in now rather than having to make up time,” said Froome, who took the race leader's jersey from Swiss veteran
Froome's relief was understandable, given how heavy the crash behind him was. It happened with a little under 60 kilometers (37 miles) remaining, forcing the stage to be neutralized and then stopped altogether shortly after — for nearly 20 minutes.
With the race moving from neighboring Netherlands into Belgium, stage three was 159.5 kilometers (99 miles) from Antwerp to Huy. It featured four short and sharp climbs but the crash took place shortly before climb No. 1 when Frenchman
Racing at tremendous speed, it was impossible for those behind to either slow down or get out of the way, and one after the other they went up, down, or sideways in a bewildering flash of colors, bobbing helmets and spinning wheels.
The end result was a tangled mess of bikes, spewed in all directions. Some riders lay on their backs in the grass and others were curled up in agony on the hot tarmac.
The 34-year-old Cancellara was one of the last to go down, leaping into the air with his bike attached to him, then landing with a thud in the grass.
He finished the stage but later pulled out of the race after hospital tests showed that he had fractured two vertebrae in his lower back.
"This is incredibly disappointing for me," said Cancellara, who was riding in his last Tour. "The team was on a high with the yellow jersey, and we were very motivated to defend it.
Bonnet was taken off on a stretcher with a brace around his neck. Dutch rider Tom Dumoulin — competing for the best young rider's white jersey — Australian veteran
As the pack up ahead waited, riders started coming back: cuts and bruises decorating their backs and legs. Cancellara grimaced in pain, Australian
The stage re-started for good with about 50 kilometers (31 miles) remaining. But it almost seemed like a training ride as no rider wanted to speed up.
Finally, about a dozen riders surged ahead.
Exhausted, the others let them go.
After taking chunks of time out of Nibali and Quintana on Sunday's rain-soaked and wind-battered second stage, Froome did it again as he accelerated in the last climb.
"It's never too early to take the yellow jersey," Froome said. "Really happy to come second and put more time on my GC (general classification) contenders."
Rodriguez and Froome clocked the same time of 3 hours, 26 minutes, 54 seconds. Frenchman Alexis Vuillermoz was third, four seconds behind them.
The day's final two climbs — 1.3 kilometers (0.8 miles) — up Cote de Cherave and the Mur du Huy featured on this year's Fleche Wallonne (Walloon Arrow) classic, which Rodriguez has previously won and where Froome crashed in this year's race.
Froome had better luck this time, gaining 11 seconds on Nibali and Quintana and 18 seconds on Contador.
"Froome is very strong and he's come here in good form," Contador said.