Marco Bielsa's side hosted the Rams at Elland Road on Wednesday night holding a 1-0 lead from the first leg at Pride Park and made the perfect start thanks to an early Stuart Dallas strike.
However, Derby levelled the aggregate scoreline thanks to goals from Jack Marriott and Mason Mount either side of the half-time interval.
A Harry Wilson penalty then gave the visitors a two-goal advantage, before Leeds pulled one back via another Dallas effort 62 minutes into the contest.
Marriott completed the scoring by adding his second seven minutes after Gaetano Berardi was sent off for the home side and Derby advanced to the final against Aston Villa, which will take place at Wembley on May 27.
Prior to the showdown between the two promotion contenders, the infamous 'Spygate saga' came back into the public eye, four months after Bielsa admitted sending a member of staff to watch Derby train ahead of a 2-0 win at Elland Road on January 11.
During the first leg of the play-off tie, Leeds supporters taunted Lampard on the sidelines with their own rendition of the classic Oasis song ‘Stop Crying Your Heart Out’ and the ex-Chelsea midfielder took the opportunity to exact revenge after yesterday's win.
Derby midfielder Duane Holmes shared a video of dressing room celebrations between the players and staff, during which Lampard can be seen leading a chorus of the same song, taking aim at Leeds supporters.
A number of Rams stars were also pictured mocking Leeds with binocular gestures referencing 'Spygate' as they celebrated in front of the Derby fans at full-time.
Lampard was asked post-match if victory over Bielsa's side was extra sweet due to the tension between the two clubs, to which he responded: "Maybe, maybe, I’m not going to lie maybe it is because I heard a lot of people saying that we’re crying over ‘Spygate’.
🕵️♂️🕵️♂️🕵️♂️ pic.twitter.com/EkELXkbyrV— Soccer AM (@SoccerAM) May 15, 2019
"I haven’t thought about ‘Spygate’ for a long time. We’ve played them, we were prepared and we got a result. Thank you."
Some Derby players even took to Twitter to rub salt into Leeds' wounds after the match, using the phrase 'I spy with my little eye' in their captions.
I spy with my little 👁 something beginning with W 👀— Martyn Waghorn (@Mwaghorn_9) May 15, 2019
I spy with my little eye, something beginning with W 🔭👁— Mason Mount (@masonmount_10) May 15, 2019