Joe Rankin-Costello opened the scoring for Blackburn on 19 minutes but the Foxes' resistance fell away after defender Calvin Ughelumba was sent off 20 minutes later.
Ben Paton and Stefan Mols made the score 3-0 before half-time while Jack Vale scored twice in three minutes at the start of the second half.
The visitors pulled one back on the hour when Kiernan Dewsbury-Hall struck from range but John Buckley and Charley Doyle both weighed in with a goal each.
Leicester's first loss since November drops them to third, four points behind leaders Everton.
A fourth win in five means Blackburn are ninth on 18 points.