Joe Quigley gave the Spireites a first-half lead before Rajovic levelled soon after coming off the bench and Dele-Bashiru snatched the late winner.
Watford head coach Valerien Ismael said: "The main thing in the Cup is always to come through, because nobody will talk about the actual game.
"We made the game complicated for ourselves and credit to Chesterfield - they played well with a nothing-to-lose mentality." Defeat was a cruel blow for Paul Cook’s side who deserved at least a replay.
The Championship side gave a first start to Rhys Healey, while Chesterfield made five changes – Liam Mandeville, Ryheem Sheckleford, Joe Quigley, Ollie Banks, and keeper Ryan Boot coming in for the National League leaders.
Watford almost took a fifth-minute lead when Yaser Asprilla intercepted a back-pass from Branden Horton but his effort was blocked by Shackleford.
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Pride at the park is perfect for Paul
EVERYONE deserved a pat on the back was Paul Warneâs verdict as his Derby County side hung on for all three points.
ACE HARRIS NETS TOP AWARD WITH GOAL RUSH
STRIKER Mark Harris has led the Oxford United assault on the second tier â and now itâs landed him the Sky Bet Championship Player of the Month award for August.
SEASIDE LATE SHOW GIVES BRUCE BUZZ
IN HIS first match back in football, new Blackpool boss Steve Bruce admitted this was a tense encounter.
CLEMENCE GETS BLUEBIRDS TO
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KARL FUMES DESPITE LATE SUB HEROICS
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PATIENCE REQUIRED OVER NEW BOY ALZATE
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DOM AIMS TO HAVE A BALL AT THE O'S...
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DEL-BOY IS CUSHTY FOR CLEVERLEY
ALTHOUGH it needed a second-half strike from Tom Dele-Bashiru to rescue a point for Watford against Coventry, Hornetsâ relieved head coach Tom Cleverley was determined not to point the finger at his slow-starting players.
MACKEMS' PERFECT RECORD IS ROO-INED
WAYNE Rooney expressed his delight after his first Championship win as Plymouth Argyle boss came by beating previously unbeaten leaders Sunderland at the death.
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