The Rams forward stepped off the bench just before half-time and scored with his first touch 33 seconds later to cancel out Stuart Dallas’ opener.
Marriott’s intervention sparked Derby’s thrilling fightback. Trailing 1-0 after the home leg and 2-1 on aggregate at half-time, quickfire goals from Mason Mount and Harry Wilson put them 3-2 ahead.
A second goal from Dallas levelled it up at 3-3 on aggregate, but Marriott skipped in for his decisive second to clinch the tie in front of a partisan Elland Road crowd in the 85th minute.
“It’s such a good feeling and I don’t really know what to say,” said the 24-year-old. “It’s just such an incredible feeling.
“I didn’t think my first touch would be putting it in the net, so that’s excellent. What a feeling and place to do it like this and a competition like this. It’s great.
“It’s up there (as one of the best moments of his life). Not the best, that was the birth of my son. Second or third, it’s up there.”
Frank Lampard’s Rams had lost only one of their final 12 games to seal the last play-off spot on the closing day of the regular season.
But after Kemar Roofe’s solitary strike in the first leg, Leeds were clear favourites to join Aston Villa in the showpiece Wembley final.
“We were the underdogs here,” Marriott said. “Everyone was saying they were expecting a Leeds v Villa final. Leeds-Villa, Leeds-Villa, Leeds-Villa.
“Villa got through the other night, fair play to them. But we’ve got to take it as motivation. We’ve proved a lot of people wrong here.
“It shows the courage in the dressing room and the desire we have got.”
Derby have reached the play-offs four times in the last six seasons, losing in the 2014 final and the semi-finals in 2016 and 2018.
But Marriott said the club is ready for top-flight football and he felt at the start of this season that this could finally be their year.
“You’ve got to have that belief or you won’t go anywhere,” he said. “You’ve got to believe at the start of the season that you’re going to get promoted.
“I saw it in the first game of the season at Reading (Derby won 2-1). Those three points meant so much to us back then.
“It’s put us where we are now. That belief in the dressing room really takes us far.”
And how can he top his Elland Road heroics? “We’re at Wembley,” he added.
“Go and win at Wembley and then we party. It’s a big, tough game and we’ll prepare properly. We’ll work and look forward to it.
“We’ve made such a big step in our season to get this far, now let’s go and finish it off.”