The emphatic result sends Liam Rosenior's side to Wembley Stadium, keeping alive their ambition of lifting the FA Cup for the first time since 2018.
It also provides a timely response after a turbulent spell marked by four straight defeats, financial concerns, and off-field distractions involving Enzo Fernandez and Marc Cucurella.
Despite Port Vale's remarkable run - having eliminated Sunderland and reached their first quarter-final in 72 years - the gulf between the sides, separated by 61 league places, proved decisive.
Chelsea wasted no time asserting dominance, with Jorrel Hato scoring after just 64 seconds following a poor punch from Joe Gauci.
Joao Pedro doubled the lead after capitalising on a defensive error, before captain Cole Palmer added a third via a deflection just before the interval.
The second half brought further punishment. Tosin Adarabioyo struck after Estevao hit the post, while Andrey Santos headed in unmarked for the fifth.
Estevao, denied twice by the woodwork, eventually got his reward after a VAR review overturned an offside call.
Late drama saw Alejandro Garnacho win and convert a penalty following a foul by Tyler Magloire, sealing the rout with the final kick.
Chelsea now turn their focus to a crucial Premier League clash against Manchester City next Sunday, as they continue their push for a top-five finish and Champions League qualification.