Ronnie Jepson's men really should have gone in front when Priskin clearly hauled Simon King down in the penalty area following a Nicky Southall corner but Gary Mulligan's spot-kick was poor, enabling Richard Lee to block the ball away with his legs.
The visitors were made to pay for that miss 11 minutes later when Priskin atoned for his error, getting across his marker to cleverly glance Rinaldi's cross from the right down and beyond Simon Royce to give the Hornets the advantage.
It was very nearly a short-lived lead though, as it took a fine goalline clearance from Cedric Avinel to prevent Mulligan from forgetting his penalty miss by netting from an acute angle.
Instead, it was the Hornets who doubled their lead in the first-half when Royce appeared to be deceived by the power of Rinaldi's free-kick from the edge of the area as it flew over his head.
The League One side's hopes of an unlikely comeback were effectively ended six minutes after the restart when Efe Sodje was sent off for elbowing Rinaldi.
And Watford confirmed their place in the second round when substitute Campana headed in his first senior goal for the club from an Anthony McNamee cross.