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.
Three minutes later Davies was involved again, this time with a header from the centre of the box which was caught by Rovers goalkeeper Jake Kean.
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.
City's veteran defender Louis Carey has been in fine form since Sean O'Driscoll took charge and he pulled off a much-needed block three minutes later from Pederson's left-footed effort.
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.
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.
Elliott, with just two goals to his name this season coming into this match, tried his luck again a minute later from 30 yards but missed the target.
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.
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.
- Sports & Recreation
- Steven Davies
- Danny Murphy