Thomas Tuchel's side had to work hard to break Palace's stubborn resistance in the semifinal at Wembley, but Loftus-Cheek's ferocious strike put them on course for a third successive FA Cup final appearance.
Mount put the result beyond doubt with a fine finish of his own, ensuring Chelsea a date with Liverpool in the final at Wembley on 14 May.
It will be Chelsea's fifth FA Cup final in the last six years as they look to make amends for losing in the showpiece against Arsenal and Leicester in 2020 and 2021 respectively.
In their 16th FA Cup final, Chelsea will aim to win the competition for the ninth time and first since 2018.
It was a welcome tonic after Tuesday's painful Champions League quarterfinal exit at Real Madrid, where the Blues scored three times to overturn a 3-1 first-leg deficit only to go out after extra time.
Tuchel has won the Champions League, Club World Cup and Uefa Super Cup in his reign, but he is yet to lead Chelsea to a domestic trophy.
With three consortiums in the running to buy Chelsea following the British government's sanctions on Russian billionaire Roman Abramovich after the invasion of Ukraine, the Blues could have a new owner by the time they return to Wembley.
Beating Palace keeps them in contention to end a troubled season with silverware, although Liverpool, who beat Premier League leaders Manchester City 3-2 in Saturday's semifinal, will provide far tougher opposition.
Tuchel made just three changes despite his players' mental and physical fatigue after the draining defeat in Madrid, leaving Thiago Silva, N'Golo Kante and Loftus-Cheek on the bench.
Chelsea had beaten Palace twice without conceding a goal in the Premier League this season, but they looked flat in the first half.