The winning strike came less than a month after Windass scored twice in the Tigers' 3-2 FA Cup defeat at Plymouth and gave Phil Brown's men ample revenge for the knockout.
It completed a miserable week for the Pilgrims, who saw star player David Norris move to Ipswich on Thursday and who have been shorn of a host of talent in the January transfer window.
Windass's goal was a soft one, coming in the one minute of time added on at the end of the first half. On-loan Manchester United striker Fraizer Campbell - watched by England Under-21 manager Stuart Pearce - created the opportunity for Ricketts to send in a low driven ball from the right. Argyle defender Krisztian Timar took a wild swipe at the ball and it went all the way to the far post where it hit Windass and dribbled over the line.
The result might have been different if Timar had not had an early goal chalked off by referee Paul Armstrong.
The Hungarian centre-back headed home compatriot Peter Halmosi's right-wing corner only for the attempt to be disallowed for apparent pushing by Rory Fallon. At best, the contact between Fallon and Hull goalkeeper Boaz Myhill was 50-50, but Fallon could make out a good case for the one being fouled.
Myhill used his hands more legitimately to punch another Halmosi corner out from under his crossbar, but that was more or less as far as Argyle's threat went.
Hull saw out the game comfortably and Simon Walton hit the outside of a post before the impressive Campbell and substitute Caleb Folan were denied only by last-gasp tackles from Mathias Doumbe and Timar.