Priskin's double and a tap-in from captain John Eustace proved enough for the second half to be a mere formality.
But following an extended lay-off for the international break, the Saints were quick out of the traps as Andrew Surman's long through ball sent McGoldrick scampering clear of a flat-footed Watford defence.
The teenage forward evaded Darren Ward and clipped the ball over Lee only to be sent crashing to the ground by the goalkeeper.
Referee Trevor Kettle decided to give Lee only a yellow as the long delay allowed doubt to creep into McGoldrick's head as he placed a poor penalty into the grateful arms of the fortunate Watford keeper.
The home side were left to rue that first missed opportunity as a short corner involving Lee Williamson and Jon Harley saw the ball arrive at the far post where Priskin was the most alert to open the scoring.
Southampton then spurned another chance to haul themselves into the game when Adrian Mariappa bundled over Ryan Smith and this time Wotton's driven penalty was saved by the feet of Lee.
Further misery was to come as Harley's 29th minute corner landed on the head of Ward, whose effort crashed off the underside of the crossbar for Eustace to bundle over the line.
Southampton continued to create and McGoldrick was again guilty of wasteful finishing when he raced clear once more but, in attempting to lift the ball over Lee, he placed it inches wide.
The result was confirmed seven minutes later when a free-kick near the corner flag by Williamson caused havoc in the Saints defence and Priskin was on hand to back-heel the ball over the line.
Southampton attempted to rally after the break but for all their possession were unconvincing in the final third and Priskin missed two good chances to walk away with the match ball.