The Blues goalkeeper put his side on the back foot when he allowed Brenden Aaronson to dispossess him inside his six-yard area midway through the first half for a simple tap in.
Further goals for Rodrigo – who nabbed his fourth of the season – and Jack Harrison cemented a famous win for Jesse Marsch's men, who claimed a first triumph over its London rival for almost two decades.
Thomas Tuchel – in the dugout despite his red card in last week's London derby draw with Tottenham – will be left to wonder just how his side were so expertly unravelled under sunny skies in West Yorkshire.
Amid a high-energy start that saw the hosts hassle their visitors on and off the ball, Raheem Sterling thought he had curled an opener in just shy of the quarter-hour mark, only for the assistant referee's flag to rule him offside.
That disallowed finish would come back to bite the Blues just beyond the half-hour when Mendy's decision to dally with a backpass saw him pay dearly as Aaronson darted in to rob the Senegal international and roll the ball into the net.
Just four minutes later, Leeds had Elland Road rocking further as they doubled their tally with Rodrigo's header, the Spaniard powering home from Jack Harrison's free-kick after Sterling had committed a foul just outside the box.
Chelsea resisted changes, and briefly it appeared as if Tuchel's men could force a comeback, but when Harrison finished off Rodrigo's knockdown with a quarter of the game to go, the result was sealed.
It was to get worse for the visitors, who ended the match a man down after Kalidou Koulibaly was shown a second yellow card for dragging down Joe Gelhardt, and Chelsea ultimately skulked from the field in the shadow of a famous Leeds win.