Neto’s superb 18-yard effort gave Chelsea an interval lead and after he struck again direct from a corner early in the second half, Brazil forward Estevao put the tie to bed just before the hour-mark.
Portugal winger Neto completed his hat-trick with 19 minutes remaining, while Championship promotion-chasers Hull never threatened to cause an upset.
Rosenior’s reign as Chelsea boss began in January with a thumping 5-1 win at Charlton in the third round and on an emotional return to the MKM Stadium – where he was a former player and manager – the Londoners cruised into the last 16.
Aside from defeats in both legs of Chelsea’s League Cup semi-final against Arsenal, Rosenior has now won eight and drawn one of his nine other matches in charge in all competitions.