Cancellara proved his credentials as Olympic and world champion
Britons David Millar and Geraint Thomas produced superb rides to finish third and fifth as Swiss Fabian Cancellara won his fourth Tour de France prologue.
Cancellara powered into the yellow jersey in 10 minutes flat over the 8.9km course in Rotterdam, eclipsing German Tony Martin by 10 seconds.
Scotland's Millar ended 20 seconds back while Welshman Thomas was 23 seconds adrift, just behind Lance Armstrong.
Alberto Contador finished sixth while Bradley Wiggins was 56 seconds back.
"After the first day of the 2010 Tour de France, Bradley Wiggins is already 20 seconds worse off than he would probably like to be, but then again so are many of the other contenders," said BBC Radio 5 live commentator Peter Slater.
"Armstrong and Contador are the big winners on day one."
Wiggins, who won the Giro d'Italia prologue in Amsterdam in May and finished fourth on last year's Tour, was sent out among the earlier starters by Team Sky in the hope that he could benefit before the forecast rain materialised.
But he ended up racing in some of the worst weather of the day and his time of 10'56" left him 34 seconds behind seven-time champion Armstrong, who looked in good form as he began his final Tour, and 29 seconds behind overall favourite Contador.
It is always nice when you beat someone as good as Brad, no matter what the conditions
The Londoner was 21 seconds slower than Martin, who was the 11th rider to complete the course in the dry, at the intermediate time-check, losing more time in the second half.
"I was pretty happy with the way I felt physically and the numbers in front of me," Wiggins said afterwards. "I didn't want to chance anything.
"I have said all along the prologue wasn't the be-all and end-all for me. I am just pleased to get round in one piece - I felt good and did what I had to do.
"I couldn't push it to the limit on the corners and risk a crash where I might have lost three or four minutes. The prologue is so insignificant in the big scheme of things - it is a matter of seconds whereas it will be minutes in the mountains."
Wiggins' team-mate Thomas, the new British road race champion, was delighted with his own effort.
"It is nice to do a good ride, especially in a race like this," he said. "People like Brad probably took it a bit easier than me on the corners because they can't risk a crash.
"But it is always nice when you beat someone as good as Brad, no matter what the conditions.
THOUGHT OF THE DAY
After the first day of the 2010 Tour de France, Bradley Wiggins is already 20 seconds worse off than he would probably like to be...Armstrong and Contador are the big winners on day one"
BBC 5 live commentator Peter Slater
"From now I just switch to being there for Brad and doing what is asked of me."
Millar, who won the prologue in 2000, described his own ride as "not so bad".
"It was good to get it out the way on a very fast course," he said. "It was not at all technical, and even with the wet roads you could really go fast."
Cancellara, who was the penultimate rider to tackle the course, made the most of the drying conditions and was six seconds up on Martin at the halfway time-check and maintained his form to the finish.
"That was a great opening for me and the team," said the Saxo Bank rider. "It's an amazing day. I'm really happy.
"It was hard waiting in the bus, I was praying that the sunshine would come. I had luck, what I also needed to win. With the rain, it did not look like it may come but the sunshine came and I rode well."
Armstrong said on the RadioShack website: "I'm happy with the result. Everything from the start of the day through to warm-up felt solid. I got a little lucky with the weather. It cleared up a little bit and I had a few dry corners. I also put some time on some of my main rivals."
The other five British riders in the Tour, Steve Cummings, Charly Wegelius, Mark Cavendish, Jeremy Hunt and Dan Lloyd, all finished more than one minute behind Cancellara.
1 Fabian Cancellara (Swi/Saxo Bank) 10 minutes, 0 seconds
2 Tony Martin (Ger/HTC-Columbia) +10 seconds
3 David Millar (GB/Garmin) +20"
4 Lance Armstrong (USA/RadioShack) +22"
5 Geraint Thomas (GB/Team Sky) +23"
6 Alberto Contador (Spa/Astana) +27"
7 Tyler Ferrar (USA/Garmin) +28"
7 Levi Lepheimer (USA/RadioShack) +28"
9 Edvald Boasson Hagen (Nor/Team Sky) +32"
10 Linus Gerdemnn (Ger/Milram) +35"
10 Brent Bookwalter (USA/BMC Racing) +35"
10 Adriano Malori (Ita/Lampre) +35"
10 Janez Brajkovic (Slo/RadioShack) +35"
10 Michael Rogers (Aus/HTC-Columbia) +35"
77 Bradley Wiggins (GB/Team Sky) +56"
113 Steve Cummings (GB/Team Sky) +1'07"
122 Andy Schleck (Lux/Saxo Bank) +1'09"
126 Charly Wegelius (GB/Omega) +1'10"
127 Mark Cavendish (GB/HTC-Columbia) +1'10"
139 Jeremy Hunt (GB/Cervelo) +1'13"
177 Daniel Lloyd (GB/Cervelo) +1'23"