Two-time world champions Davis and White -- seeking a first ice dancing gold for the United States -- skated a foxtrot and quickstep to "My Fair Lady", scoring 78.89 points, with Monday's free dance to come.
Reigning Olympic champions Tessa Virtue and Scott Moir of Canada achieved 76.33 for their skate to "Dream a Little Dream", "Muskrat Ramble" and "Heaven".
It is the latest round in an ongoing rivalry on the ice going back to junior days between the two couples who train together in Detroit with Russian coach Marina Zoueva.
White said: "We were just in our zone, so we could go out and skate like that. It felt awesome. When we were going out, we said, 'Let's do it for each other'."
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All eyes at the Sanki sliding centre were on Jamaican crowd pleasers Winston Watts and brakeman Marvin Dixon in the first two heats of the two-man bobsleigh but the underdogs could only limp in last.
The Jamaican team -- whose predecessors inspired the movie "Cool Runnings" with their exploits at the 1988 Calgary Games -- were out of their depth, coming 30th out of 30 sleds, with two heats still to go.
"We're still here, we're still competing. Just watch us tomorrow," he added. "I want to show the world that Jamaica is still alive. I guarantee to slide faster tomorrow, and I love you guys, I love you all."
- 'I am floating and feeling great' -
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Earlier, in the mountains above Sochi, Norway's Kjetil Jansrud won a shock gold in the Olympic super-G as the big guns of alpine skiing again failed to fire.