Roberto Pereyra appeared to have put the game out of reach when he scored a third for last season’s beaten finalists after 34 minutes.
But in a stunning second half, Tranmere pulled one back shortly after the hour mark when Connor Jennings’ disallowed offside goal was overturned by VAR.
Pereyra was then sent off for foul play to cap a miserable second half for the Vicarage Road side.
With more than one eye on Premier League survival, Nigel Pearson rung the changes for the visit of the League One outfit, with only Craig Dawson and Chalobah retained from the side that ran out 2-1 winners over Wolves on New Year’s Day.
Dele-Bashiru, the Nigeria Under-20 international, signed a six-year deal at Watford last summer after he was released by Manchester City. His appearance here was only his second for the club, but just 12 minutes into his full debut, the 20-year-old midfielder was celebrating his first senior goal.
Following a short corner, Chalobah laid the ball on to Dele-Bashiru, who was afforded too much time to set himself before unleashing a fine 25-yard drive past a helpless Aaron Chapman in the Tranmere goal.
Rovers, fighting to retain their status in the third tier, were still recovering from Dele-Bashiru’s opener when the rampant hosts added a second.
The impressive Isaac Success powered his way into the visitors’ box, and – as the Tranmere defence tried to clear their lines – the ball fell to Chalobah on the edge of the penalty area. The midfielder showed good composure to dispatch his side-footed strike into the back of the Tranmere net.
Following their 200-mile journey from the north west, the travelling fans remained in good voice only for Pereyra’s strike 11 minutes before the interval to seemingly kill the third-round tie.
But Jennings gave the visitors a glimmer of hope with his header after 66 minutes. The goal was originally ruled out for offside, but then rightly overturned following a VAR check.
Moments later, Jennings nearly scored a second but debutant goalkeeper Daniel Bachmann tipped his lobbed effort over the crossbar.
Bachmann, Watford’s third-choice stopper, then became the villain when he came to collect a Tranmere free-kick only to fumble his effort with defender Monthe scoring on the swivel.
VAR took centre stage for a second time in a dramatic finale.
Referee Graham Scott had given the visitors only a corner after he deemed Barrett had nicked the ball away from Blackett-Taylor. But replays showed the 20-year-old defender only took the man with Scott pointing to the spot.
Mullin fired home from 12 yards to send the travelling fans wild as the League One outfit secured the most unlikely of replays before Pereyra saw red.