The Spaniard was awarded a controversial second-half goal - which appeared not to have crossed the goal-line on replays - before turning provider for Ramires to hit Chelsea's third.
Though the Blues were pegged back to 2-1 by a Gareth Bale strike, they scored a further three goals to ensure a final date with Liverpool on May 5.
Mata took to Twitter following the match, saying: "We'll play the FA Cup final! The whole team played very well. This gave us a lot of confidence for Wednesday match. Wembley, unbelievable.’’
The west London side must now prepare for a midweek Champions League clash with Barcelona at Stamford Bridge.