Substitute Richard Hughes was shown two yellow cards in the space of four second-half minutes, but Rovers were already in a commanding position thanks to a first-half brace from Rhodes and a goal from Leon Best.
Another Cherries substitute, Ryan Fraser, pulled a goal back in the 74th minute after being put clear by new signing Tokelo Rantie but it was too late to stop Blackburn picking up a 3-1 win - their first on the road this season.
Blackburn surged into a 3-0 lead inside 41 minutes.
Best created the first goal in the 10th minute with his low cross being met by a diving header from £8million striker Rhodes, who scored for the seventh time in nine matches.
Best, who had a loan spell at Bournemouth when he was a Southampton player, added the second in the 24th minute with a shot from 15 yards after Corry Evans had opened up the home defence.
Rhodes was on the scoresheet again in the 41st minute when Josh King was brought down by a lunging tackle from Tommy Elphick in the penalty area.
Rhodes stepped up to send Ryan Allsop the wrong way with his spot-kick to give Rovers an unexpectedly impressive lead at the break.
Bournemouth had lost midfielder Shaun MacDonald with a knee injury in the 33rd minute and Hughes, his replacement, picked up two bookings after the restart - the latter for a foul on Evans - to find himself heading back down the tunnel.
Bournemouth's luck looked to be finally be out when Marc Pugh's effort hit the inside of the post in the 58th minute, but Blackburn had never really looked like losing their lead anyway.
Elphick nearly redeemed himself for conceding the penalty when he volleyed an effort towards goal in the 66th minute, but Jake Kean pulled off a fine save.
Bournemouth finally got their consolation goal when record signing Rantie turned brilliantly past Grant Hanley to send through Fraser, who poked it past Kean in the 75th minute.
Rhodes nearly took home the match ball, but his shot on the stroke of full-time was inches away from making the final score 4-1.