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.
The visitors, 2-0 winners at home to Watford on Tuesday night, picked off where they left off at Ewood Park with Steven Davies' 25 yard free-kick skimming the top of the net after just six minutes.
But 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 Jake 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, with Sam Baldock's flick setting up Davies but his effort from 18 yards crashed off the post.
City, looking to close the four-point gap between themselves and safety, started the second in the same fashion as the first with Brendan Moloney's effort being blocked by Jason Lowe and Marvin Elliott, starting in place of captain Cole Skuse, heading straight at Kean.
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 in only 157 appearances, latching onto Murphy's long ball from his own half before rolling the ball past Heaton.
The home side were enjoying plenty of possession and carving out chances, Kazim-Richards curling over the bar as his side cruised to their second win over Bristol City in 2013.
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