Rovers started the match brightly with Jordan Rhodes missing a one-on-one, but it was Stanley's Piero Mingoia who opened the scoring.
Blackburn's veteran midfielder David Dunn soon equalised but, just after the break, Northern Ireland Under-21 international James Gray rifled home to make it 2-1.
Tom Cairney took advantage of a defensive mix-up to bring the scores level and despite Gray hitting the post late on, neither side was able to find a winner.
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