The win earns Rovers a two-legged tie against Aston Villa, the first leg at Ewood Park.
Blackburn more than deserved the win after for their dogged performance taking an early lead through Nico Kalinic.
Chelsea for their part rarely impressed in the first half with only a Salomon Kalou header troubling the Rovers goal.
Blues boss Carlo Ancelotti not surprisingly made three substitutions for the second period and it paid immediate dividends.
Didier Drogba powered in a headed equaliser and within four minutes the visitor's had taken the lead through Kalou.
But Blackburn restored parity just after the hour when Brett Emerton's cross eluded the Chelsea keeper Henrique Hilario and found the back of the net.
With no further scoring the game went into extra time and Benni McCarthy put Rovers back in front from the penalty spot after David Hoillet was fouled, but it was 3-3 in the dying seconds when Paulo Ferreira scored after a poor Robinson clearance.
But the England international was to make amends by making the crucial spot kick save from Kakuta.