On-loan MK Dons centre-back Gary MacKenzie gave Blackpool a 64th minute lead as Rovers once again failed to convince.
But Scotland international striker Rhodes secured a share of the spoils with his 24th Championship goal of the season.
Tom Ince and substitute Elliot Grandin came close to sealing the points for Paul Ince’s men, but both teams edged five points clear of the relegation zone.
David Dunn fizzed a 25-yarder over on the back of a driving run from Joshua King as Rovers threatened to shake their early lethargy.
Matt Phillips flashed a long-range drive past the post with Blackburn goalkeeper Jake Kean scrambling in the 35th minute.
Rovers started the second half on the front foot and David Jones rounded Matt Gilks but fired over.
But Blackpool began to push Rovers back and Kean palmed away when Ludovic Sylvestre shot through a crowd of bodies.
MacKenzie then reacted quickest to smuggle home at the near post after Kean touched Alex Baptiste’s header from Tom Ince’s right-wing corner away from the goalmouth.
The equaliser came in the 79th minute with set-piece vulnerability on display once more – Todd Kane heading across goal from Lee Williamson’s chip into the box after Pool failed to clear for Rhodes to nod home and end a six-game goal drought for club and country.
Blackpool came closest to stealing victory as Kean parried Ince’s shot at the end of a menacing run and tipped over Grandin’s header.