Palace led through Stephen Dobbie but Ian Holloway's men will look uncomfortably over their shoulders from fifth position next weekend, with Bolton, Nottingham Forest and Leicester all within touching distance.
Rhodes was presented with Rovers' player of the season award before kick-off and scored his 27th goal since joining from Huddersfield in August to ensure Ewood Park caretaker boss Gary Bowyer can breathe easily.
Opportunities were few and far between until midway through the half when Blackburn established themselves as an attacking threat - Josh King's cutback narrowly evaded Nuno Gomes after a driving run and, moments later, Rhodes fired over on the turn.
Back came Palace and Blackburn defended a flurry of corners successfully only to see their good work undone in the 28th minute.
Dobbie collected Aaron Wilbraham's flick-on and got the better of Grant Hanley to produce a smart finish.
The former Swansea forward almost doubled his tally six minutes later, watching a free-kick fly past the post from 25 yards with Rovers goalkeeper Grzegorz Sandomierski at full stretch.
Damien Delaney then passed up a chance as Hanley failed to clear another set-piece and the Eagles defender would soon rue his profligacy.
King released Rhodes following a fine pass from Josh Morris and the Scotland international burst clear to deftly lift the ball over Julian Speroni and home from an acute angle.
Glenn Murray and Mile Jedinak hit the crossbar for the visitors during the second period but Holloway's men were unable to find an invaluable winner.