In a general election match-up between McConnell and presumed Democratic nominee Alison Lundergan Grimes, McConnell takes 48 percent of likely voters, while grimes takes 40 percent. Twelve percent are undecided.
Bevin, too, would defeat Lundergan Grimes, but narrowly, 35 percent to 30 percent.
And the incumbent is also seen favorably by more than half of Kentucky voters, though 32 percent have a very unfavorable view of the senator.
Lundergan Grimes is seen favorably by 35 percent of voters, while another 40 percent view her unfavorably, and a quarter haven't yet formed an opinion on her.
That's an increase from a month ago, when she was seen unfavorably by only 25 percent of voters, an indication early attacks on the candidate from a super-PAC backing McConnell, as well as a campaign rollout that many critics said she botched, have hurt her standing in the eyes of voters.
The survey was conducted on Tuesday and Wednesday, with Bevin announcing his campaign on Wednesday. Two-thirds of voters have no opinion of the Tea Party candidate yet, but 21 percent already hold an unfavorable view of him, and 15 percent hold a favorable view.
The survey indicates, however, that voters are split on reelecting McConnell. About 40 percent each say they'll be definitely voting for McConnell and definitely voting for someone else, while 20 percent of voters say they would consider voting for someone else.
And a majority of likely voters say McConnell's job performance in Congress has been only fair or poor, indicating McConnell's challengers may still have an opening in the coming months of the campaign.
The survey was conducted among 624 likely voters from July 23-24 and has a margin of error of plus or minus 3.9 percentage points.