A Rovers XI lost by the same scoreline to Accrington on Saturday after defeating Fleetwood earlier on the same afternoon, but boss Steve Kean was subjected to a poor display from a strong line-up and familiar calls for his head from the travelling support.
Error-strewn performances from both sides meant chances were at a premium in the first-half, with Dale striker George Donnelly coming closest to breaking the deadlock as he thrashed a 30-yard drive narrowly beyond the post.
Blackburn's veteran ex-Portugal star Nuno Gomes was withdrawn at the interval in favour of David Dunn, but strike partner David Goodwillie enjoyed a productive start to the second period as he twice burst clear of the Rochdale defence.
On the first occasion home goalkeeper Josh Lillis dashed out of his area and appeared to blatanty handle as the Scot rounded him. The referee's assistant was well-placed but unmoved and moments later Goodwillie played in Fabio Nunes, who dinked over the onrushing Lillis and saw Luke Watson clear superbly off the line.
Watson's fellow trialist then brought the save of the night from Jake Kean, but Rovers' substitute goalkeeper could do nothing as his defence hesitated under Reece Gray's searching ball and Thompson's shot evaded the efforts of Grant Hanley in the goalmouth.