Nevertheless, Blackburn initially responded well to the setback and came close to equalising on the nine-minute mark.
Their momentum petered out and City almost doubled their lead on the half-hour mark when Anthony Pilkington's drive deflected narrowly wide of Raya's post.
It was Rovers who finished the half on top, as Shane Duffy spurned a good chance to grab a timely equaliser but he smashed over the bar from close range as the visitors survived.
Gary Bowyer's side retained that momentum throughout the break as the hosts laid siege to Cardiff's goal in the first 15 minutes of the second period.
First, Delfouneso's deflected half volley came back off the crossbar, before Hanley inexplicably missed the target with a header from two yards out.
However, the Rovers captain had the last laugh as he found himself unmarked at the near post, before side-footing home following a scramble to salvage a point for his side.
Having come into the clash in 14th, the Welsh side move one place up the table, while Blackburn, who were 17th, now sit 16th.