Crosswinds and crashes caused several splits as the peloton made its way through heavy rain on a 166-kilometre ride from Utrecht, with Froome and Contador ending up in a small leading group that also included American Tejay van Garderen as they finished one minute 28 seconds ahead of the main pack.
In that pack was defending champion Vincenzo Nibali, Colombian Nairo Quintana and France’s Thibaut Pinot, who could only limit the damage after being trapped behind on a stage that went along the North Sea.
Greipel was the fastest in the finishing straight, outsprinting Slovakian Peter Sagan and Fabian Cancellara, with the Swiss taking the overall leader’s yellow jersey from Australia's Rohan Dennis.
Pre-stage favourite Mark Cavendish of Britain could only manage a disappointing fourth place.
Briton Froome, the 2013 Tour champion, crashed out of the Tour on the fifth stage last year, while Spain's Contador, who is attempting a rare Giro d'Italia/Tour double, abandoned his 2014 race after breaking his shinbone in a crash.
"This a huge advantage for us to sit in this position after one flat day out on the road," Team Sky rider Froome told reporters.
"This is a three-week race and things do change on a daily basis. We’re ahead today but who knows what’s in store for us for the rest of the week,"
Contador, of the Tinkoff-Saxo team, said: "There are days like this when you’re very happy to have team mates like mine."
Froome is 10th overall, 48 seconds behind Cancellara, who is wearing the yellow jersey for the first time since 2012, while Contador sits in 14th place one minute off the pace.
"It was almost like a one-day classic race," Cancellara, whose season had been hampered by a severe back injury, told reporters.
Van Garderen, one of the main contenders behind the Big Four of Froome, Contador, Nibali and Quintana, is eighth -- four seconds ahead of Froome.
Pinot, the most impressive pre-race favourite in Saturday’s opening time trial, is now 2:07 behind Cancellara with Nibali (2:09) and Quintana (2:27) further behind.
"The race is still long, with surprises every day, it was the case today," said Pinot.
They will all have a chance of revenge in Monday’s third stage, which finishes up the short but punishing climb to the Mur de Huy.
(Editing by Mark Meadows; mark.meadows@thomsonreuters.com; +44 20 7542 7933; Reuters Messaging:; mark.meadows.reuters.com@reuters.net)
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