McCain leads with 51.5 percent of the support of likely voters over Kirkpatrick’s 40 percent, the poll from Arizona Republic/Morrison/Cronkite News found.
The poll found the five-term senator has an advantage among all age groups, and leads in the state’s two largest counties, Maricopa and Pima.
The poll was conducted after McCain withdrew his endorsement of Republican presidential nominee Donald Trump after the video that showed Trump making lewd comments about women surfaced. McCain was one of several dozen Republican members of Congress to withdraw support.
A RealClearPolitics average of polls taken from August 18 through Oct. 4 has McCain up by 16 points.
In the presidential race, Democrat Hillary Clinton is holding on to a small lead, the poll showed, but 20.7 percent of those surveyed said they hadn’t yet decided who they would vote for.
First lady Michelle Obama, independent Sen. Bernie Sanders of Vermont and Clinton’s daughter Chelsea are campaigning this week across Arizona for Democratic hopefuls.
The poll surveyed 587 likely Arizona voters from Oct. 10 through Oct. 15. There was a margin of error of 3.7 percentage points.