The Whites, a goal up from the first leg at Pride Park, took the lead at Elland Road on Wednesday night when Stuart Dallas tapped in after Liam Cooper's header had hit the post.
Jack Marriott then drew Derby level with his first touch before half-time after a mix-up at the back between Cooper and Leeds goalkeeper Kiko Casilla.
Mount and fellow Premier League loanee Harry Wilson netted after the break - the latter a penalty - only for Dallas to drift in and fire Leeds back level on aggregate.
Leeds defender Gaetano Berardi was then sent off for a challenge on Bradley Johnson before Marriott edged Derby back in front with a composed finish to claim a 4-3 aggregate win.
Mount, on loan from Chelsea, tweeted the following message after the game:
I spy with my little eye, something beginning with W— Mason Mount (@masonmount_10) 15 May 2019
Some Derby fans responded on the social media platform, loving what the talented 20-year-old had posted:
Stay forever— Derby Lad (@derby_lad) 15 May 2019
Wembley Wembley we’re the famous Derby County and we’re off to Wembley⚽️— Bigsheep (@Bigsheep10) 15 May 2019
Hi Mason, I was wondering if you could officially adopt me— harry (@HarryForsyth23) 15 May 2019
Love you ❤️❤️❤️❤️— Barnaby & Chris ️ (@AmbroseBarnaby) 15 May 2019
Banter— Andrew Clarkson (@Andrew_Clarkson) 16 May 2019
.... W,W,Will be staying @dcfcofficial next season? Please stay lad, you'll develop more if you stay and get promoted than go back to West London....— Sozzled (@JK_Cunningham) 15 May 2019
Your just to good to be true I cant take my eyes of you lmao— ⚽GemDCFC⚽ (@svengem2011) 15 May 2019
Good lad Mason— rosa (@dcfcrosa) 15 May 2019
Derby, who become the first team to lose the first leg of a Championship playoff semi-final at home and still go on to reach the final, will face Aston Villa at Wembley on Monday 27 May.
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