The masked striker headed home an Aron Gunnarsson cross in the 59th minute to bring the Sky Blues a lucrative home tie with Chelsea.
Blackburn boss Sam Allardyce named a totally different side to the one which had lost at Old Trafford but was still rewarded as his side looked set to make the most of their last-minute escape in the original tie.
Rovers looked technically superior to their Championship opponents but they failed to make their first-half possession count.
They could have taken a first-minute lead when a slip from Ben Turner allowed in Carlos Villaneuva whose shot was saved low down by Keiren Westwood.
But for all their slick midfield work, the Premiership side were too laboured in their build-up and were largely restricted to long-range efforts.
Tugay and Jason Roberts both sent efforts flying just wide of goal but highly-rated Westwood had precious little to do.
At the other end the chances may have come less frequently but were far more clear-cut.
Elliott Ward met a Danny Fox corner with perfect timing in the 19th minute but with a clear sight of goal managed to direct his header wide of the target.
Ten minutes later Best nodded the ball through to his strike partner Clinton Morrison but the veteran was on the stretch and sliced the ball wide of goal.
Coventry started the second half brightly and their goal was deserved. Jordan Henderson, on loan from Sunderland, had just made a superb break before delivering a poor cross.
But the disappointment was only temporary. From the resulting throw-in Gunnarsson put in a far superior cross and Best was able to ghost in - like a phantom - and head the ball neatly home.
Chris Samba could have spoiled the Ricoh rave deep in stoppage time when he strained to reach a cross only for his header to drift wide of goal.