The poll, conducted by Marist College's Institute for Public Opinion (search) in conjunction with New York City television station WNBC, gave the former first lady 50 percent to 41 percent for Rice.
Clinton, McCain and Giuliani are all considered potential 2008 presidential candidates. Rice has said she will not run.
The poll, mirroring other recent national surveys, had Clinton as the clear front-runner for the 2008 Democratic nomination, favored by 41 percent of her party's voters to 17 percent for Sen. John Kerry of Massachusetts and 14 percent for former Sen. John Edwards of North Carolina, Kerry's running mate in 2004.
Asked about Clinton's political leanings, 39 percent of voters said she was too liberal, while 46 percent said she was about right.
"She remains a controversial figure when she moves out from the Democratic primary sweepstakes," Marist pollster Lee Miringoff said.
On the Republican side, Rice, Giuliani and McCain were about tied for the GOP nomination, each attracting about 20 percent of the vote.
But with Rice out of the mix, Giuliani, the former New York City mayor, was favored over the senator from Arizona, 31 percent to 24 percent.
No other Republican topped single digits.
The poll had McCain leading Clinton, 50 percent to 41 percent. Giuliani was ahead of the former first lady, 50 percent to 43 percent.
Voters were divided over electing a woman as president. Twenty-six percent told pollsters they were likely or very likely to vote for a woman, while 28 percent said they were not likely to vote for a woman.
They were also divided on whether Clinton should run for president, 48 percent in favor and 49 percent opposed.
Marist's telephone poll of 827 registered voters was conducted Oct. 12-13 and Oct. 17 and had a margin of error of plus or minus 3.5 percentage points.