The 22-year-old scored for the fifth successive game just before the half-hour mark before latching onto Danny Murphy's pass and firing home with typical accuracy to secure the points for Rovers.
Michael Appleton's men were just inches away from breaking the deadlock with their first real chance in the 13th minute as they looked for their first Championship win at home since New Year's Day.
After Colin Kazim-Richards was hauled down Morten Gamst Pedersen stepped up and curled a left-footed free-kick off Tom Heaton's crossbar.
Winger Paul Anderson grabbed a vital goal in midweek and missed a huge chance to net for the second time in five days when Stephen Pearson sent him one-on-one with Kean but he fired over the crossbar.
At the other end Markus Olsson missed the target after a set-piece fell at his feet. But Rhodes then showed him how it is done, finding the bottom corner for his 17th of the campaign after a Pederson cross broke to the Scotland striker two minutes before the break.
The woodwork was then rattled for the second time in the first 45 on the stroke of half time, Sam Baldock's flick setting up Davies but his effort from 18 yards crashed off the post.
As the game passed the hour mark Rhodes came close to doubling his tally for the afternoon with a header from Bradley Orr's cross which fell wide of the left-hand post from inside the box.
But the former Huddersfield man did not have to wait long for his 100th league goal, latching onto Murphy's long ball from his own half before rolling the ball past Heaton.
A minute later Scott Dann nodded over the bar from six yards out as Blackburn looked to score three goals for the second time in a week.