The first half lacked the cut and thrust of a traditional cup tie with both sides spending the majority of the opening 45 minutes feeling each other out and throwing the odd testing punch, without really threatening to land a telling blow.
However, it was Watford that did just that after 28 minutes to take the lead for the first time at home in almost two months - an incredible statistic for a team being kept off top spot in the Championship by goal difference only.
The goal was borne out of a run into the penalty area from Palace old boy Jobi McAnuff, and Shittu rose highest in the near post area to meet Lee Williamson's inswinging corner and head firmly past Scott Flinders to net his sixth of the season.
Watford should have been given a great opportunity to double their lead within 60 seconds of the restart when Jose Miguel Fonte clearly handled to prevent Darius Henderson from heading back across goal, but referee Lee Mason and his assistants missed what the majority inside Vicarage Road saw.
However, the Hornets continued to turn the screw and deservedly scored a second after 65 minutes with a virtual carbon-copy of their first, albeit from the other side of the pitch.
This time Jordan Stewart swung in a corner from the left and Shittu pulled off his man in the six-yard box to head down and past Flinders.
Such was Watford's superiority, it took until stoppage time for the visitors to muster their first meaningful on-target attempt, but Richard Lee proved more than a match for substitute Victor Moses' effort.