Mason Mount then converted less than a minute into the second half, followed by a penalty from Harry Wilson, and although Dallas scored a second to make it 3-3 on aggregate, Marriott won a thrilling tie five minutes from time.
Relive how the entertaining match, which saw both sides have a player sent off, unfolded with Sports Mole's live text coverage below.
None of the previous 17 teams to have won the first leg of a second-tier playoff semi-final away from home has failed to progress to the final.
Who will join Aston Villa, penalty-shootout winners against West Bromwich Albion last night, in the Wembley final? We are about to find out!
STARTING XI: Casilla; Ayling, Berardi, Cooper, Dallas; Hernandez, Shackleton, Phillips, Klich, Harrison; Bamford
SUBS: Brown, Clarke, Struijk, Gotts, Jansson, Bogusz, Peacock-Farrell
STARTING XI: Roos; Bogle, Keogh, Tomori, Malone; Holmes, Johnson; Wilson, Mount, Lawrence; Bennett
SUBS: Evans, Cole, Carson, Knight, Jozefzoon, Huddlestone, Marriott
The Whites were in front 24 minutes in when Kalvin Phillips' free kick went right the way through the box, hit the post and Stuart Dallas was quickest to react to the rebound four yards out.
Klich hit the crossbar with a heavily deflected effort and Patrick Bamford, earlier booked for trying to con the officials by going to ground in the box, had a tame effort kept out from the edge of the box.
Less than a minute after coming on for Duane Holmes, Jack Marriott profited from a terrible mix-up at the back by converting into an empty net once Liam Cooper and Kiko Casilla failed to deal with a simple flick-on, rolling the ball into an unguarded net from his first touch.
LEEDS SUBS: Brown, Clarke, Struijk, Gotts, Jansson, Bogusz, Peacock-Farrell
DERBY SUBS: Evans, Cole, Carson, Knight, Jozefzoon, Huddlestone
They become the first ever side to lose the first leg of a Championship playoff semi-final on home soil and still progress through.
As for Leeds United, who led 2-0 on aggregate with pretty much a quarter of the two-legged tie to play, they must do it all over again next season - with or without Marcelo Bielsa