A side starting the day bottom of the league has not beaten the team at the top since February 2011, and Norwich never looked likely to halt that run at Stamford Bridge as Thomas Tuchel's side cruised to its biggest win of the season with ease.
Mount and Callum Hudson-Odoi got things started with their first league goals of the campaign, with Ben Chilwell scoring for a fourth successive top-flight match after fellow wing-back Reece James got in on the act.
Max Aarons's own goal and Ben Gibson's red card made life even more miserable for Norwich, with Mount doubling his tally from the spot before rounding off his hat-trick in stoppage-time.
It took Chelsea just eight minutes to take the lead, as Mount allowed Jorginho's lay-off to run across him before planting a firm strike into the bottom-left corner.
Mateo Kovacic's weighted throughball teed up Hudson-Odoi for a cool finish across Tim Krul 10 minutes later, with Mount turning provider for Chelsea's third, sliding a perfect ball through to James, who chipped in with aplomb.
After making an error that allowed Milot Rashica to test Edouard Mendy, Chilwell quickly atoned at the other end, drilling in a low finish to continue his brilliant scoring form.
Aarons's deflection on Hudson-Odoi's cross-shot did for Krul, who spilled over his own line, before Gibson, only 10 minutes after he had first been cautioned, dived in late on James.
Mathias Normann's handball handed Chelsea a spot-kick and, though Krul initially saved Mount's effort, the goalkeeper had come off his line, and Norwich's goalkeeper was unable to keep out the second attempt.
There was time for one more, Ruben Loftus-Cheek beating the offside trap and cutting back for Mount to slot in his third.