The home side came within inches of taking a 15th-minute lead, but when Owen Garvan's free kick evaded everyone in the box, it rebounded off the far post and away to safety.
Ten minutes after the break, Hanley was shown a straight red card for hauling Morison down, and Shaun Williams made no mistake from the spot to put the hosts 1-0 ahead.
The goal seemed to give the hosts a boost in confidence, as Garvan and McDonald both sent powerful efforts narrowly over.
However, Blackburn levelled with 25 minutes remaining when Michael Keane rose highest from a corner and nodded home.
Keane almost got the winner with another headed effort in the 78th minute, but Forde stretched to tip the header round the post.
All of Blackburn's hard work seemed to have come undone when Simeon Jackson netted from the penalty spot in the 88th minute, but substitute Joshua King stabbed home from close range to rescue a dramatic point for the visitors.