Former Chelsea and England midfielder Frank Lampard is now one game away from taking the Rams back into the lucrative Premier League in his first season as a manager, with Midlands rivals West Bromwich Albion their opponents at Wembley on May 27.
Leeds, already 1-0 up from the first leg, scored first in front of their own fans at Elland Road on Wednesday.
But Marriott's first goal seconds before half-time got the Rams back into contention and he settled a match which ended with both sides down to 10 men by scoring again five minutes from full-time.
Derby's victory was all the more impressive given Lampard's sixth-placed side had only just scraped into the playoffs.
Wednesday's match between two of English football's leading clubs of the early 1970s came after Leeds' defeat of Derby in January was overshadowed by the 'spygate' affair that saw manager Marcelo Bielsa admit he had sent a member of his staff to 'spy' on a Rams training session before the game.
Leeds took a 24th-minute lead on the night through Stuart Dallas after Kalvin Phillips' free-kick came back off the post.
Derby though equalised on the night just before half-time when substitute Marriott capitalised on a mix-up between Leeds defender Liam Cooper and goalkeeper Kiko Casilla moments after coming on.
They draw level on aggregate straight after the break when Harry Wilson played in Mason Mount, who cut inside from the left and beat Casilla.
Derby then went ahead in the tie for the first time in the 58th minute when Cooper needlessly conceded a penalty following a pull on Mason Bennett in the area, with Wilson scoring from the spot.
Derby's 3-2 aggregate lead did not last long, however, with Dallas scoring his second goal of the game when he struck a precise shot into the far corner.
Leeds were reduced to 10 men 12 minutes from time when Gaetano Berard's reckless two-footed challenge on Marriott saw him sent off.
Derby's winner arrived in the 85th minute when Marriott charged through on goal and dinked the ball over Casilla just before the keeper could get to the ball.
Scott Malone was then sent off in stoppage time but his exit came too late for Leeds to snatch a late leveller.