Michael Appleton - who led the Seasiders to a 2-0 victory over Rovers in December before taking up the reins at Ewood Park a month later - was sacked last week to leave Gary Bowyer in caretaker charge, as he was following Henning Berg's similarly brief tenure earlier in the campaign.
Such chaos behind the scenes under controversial owners Venky's has been reflected by dismal performances on the field and on-loan MK Dons centre-back Gary MacKenzie gave Blackpool a 64th minute lead as Rovers once again failed to convince.
MacKenzie reacted quickest to smuggle home at the near post after Jake Kean touched Alex Baptiste's header from Tom Ince's right-wing corner away from the goalmouth.
They looked set to rue earlier missed chances by David Jones and Josh King but Scotland international striker Rhodes secured a share of the spoils with his 24th npower Championship goal of the season.
Todd Kane headed across goal from Lee Williamson's chip into the box after Pool failed to clear and Rhodes nodded home to end a six-game goal drought for club and country.
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 npower Championship relegation zone having shared very different ambitions at the start of the season.