Watford were soon two in front as former Palace winger McAnuff delivered a deep cross which Cork headed back across Julian Speroni and into the far corner.
The home side were good value for their lead, but Palace hit back after the interval as Alan Lee headed John Oster's deep free-kick back across goal for Hill flick in from 10 yards.
Spurred on by the goal Palace began to dominate. However, they failed to convert their superiority into goals and were made to pay as Hoskins planted a powerful left-footed strike home to restore his side's two-goal advantage.
McAnuff again turned provider for Watford's fourth, running the whole length of the pitch before squaring for Rasiak who curled the ball beyond Speroni into the top corner.
Palace never gave up and Danns scrambled in eight minutes from time before Ifill's injury time consolation.
Watford assistant manager Dean Austin: "We need to use this as a platform. The Cup is not a hindrance for us, it's our first win in a while and we can work from here.
"We know there are goals in this team and we scored some excellent goals today but the problem all season has been conceding too many at the other end.
"We conceded territory and the ball was flicked on and they were first to all the bits and pieces."
Crystal Palace manager Neil Warnock on 23-year-old referee Michael Oliver: "I find it difficult to understand how they give referees Championship football at 23.
"I don't see how they can have the understanding of the game at that age. The way they are going he will be in the Premier League next year.
"We are pushing young referees because we haven't got a great group at the top. Young referees should have experienced linesman and I was hoping for a Premier League referee today."
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