Colin Kazim-Richards tried a speculative effort towards the end of the half, but his low drive skimmed narrowly wide.
Kazim-Richards came close to breaking the deadlock again in the second half, this time through a flicked header, but his effort was straight at Almunia.
Rhodes was the next to threaten for the hosts, getting on the end of Olsson's cross, but his header was over the bar.
Rovers were handed a great chance to take the lead with 10 minutes left when Thomas Hoban was adjudged to have handled the ball inside the box, but Kazim-Richards's penalty hit the bar and went over.
Blackburn finally found the breakthrough in the second minute of injury time when Rhodes latched on to a loose ball inside the area before firing past Almunia to give his side all three points.