The defeat ended the holders' hopes of becoming the first club since Blackburn Rovers in 1886 to win the FA Cup three times in a row.
The result appears to have condemned Arsenal to end the season without a trophy as they face elimination from the Champions League next week, unless they manage to overturn a two goal deficit against Barcelona, and they trail Premier League leaders Leicester City by eight points with only nine games left.
Arsene Wenger's men were left to rue a host of missed chances as Watford opened up a 2-0 lead in the second half with goals from Odion Ighalo and Adlene Guedioura.
Danny Welbeck pulled a goal back for Arsenal in the 88th minute but it was too late to change the result.
Watford go into the semi-finals alongside Premier League sides Everton and Crystal Palace.
(Reporting by Jamie McGeever, editing by Pritha Sarkar)
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