Of likely voters, 42 percent said they favored Mourdock, compared with 40 percent for Donnelly. The remaining voters said they were undecided or did not plan to vote for either of the major party candidates.
Overall, likely Indiana voters lean Republican by about 13 percentage points, based on Rasmussen's figures, tilting his poll further to the right than other surveys. By comparison, polling firm Gallup gives Republicans a 5-point advantage among likely Indiana voters.
Democrats trumpeted the poll as proof that mainstream Hoosier voters would reject Mourdock's hard-line conservative views, as they predicted after the tea party favorite beat six-term Sen. Richard Lugar in the primary.
"The Rasmussen poll has a built-in 15-point lead for Republicans, yet we find ourselves in a dead heat," said Indiana Democratic Party spokesman Ben Ray. "It shows Hoosiers are rejecting Richard Mourdock's tea party ideology."
One takeaway from Rasmussen's poll is that self-described moderate voters favor Donnelly by 27 points. And 8 percent of Republican voters said they preferred Donnelly, while only 2 percent of Democrats said they favored Mourdock.
But Mourdock's campaign manager, Jim Holden, said Donnelly had failed to gain ground on his opponent despite burning through more than $1 million. Holden predicted undecided voters would break toward Mourdock in the campaign's final three months.
"Once voters learn that Joe Donnelly has been a reliable vote for President Obama's economic policies, including Obamacare and the failed stimulus spending, we believe that the overwhelming majority of the undecided voters will break toward us," Holden wrote in an email.
The Rasmussen poll shows a majority of Hoosiers still favor repealing President Obama's health care law, which Mourdock has made a key issue in his campaign. According to the poll, 54 percent of likely voters would like to see the law repealed.
Mourdock routinely hammers Donnelly for supporting the law, nicknamed "Obamacare" by opponents. Donnelly voted for the law in 2010 but has said he opposes parts of it, including a tax on medical devices.