A cagey goalless draw in the first leg at Carrow Road left the tie in the balance, yet after just seven minutes here, the deadlock was broken.
Shouldering the burden of expectation from a fervent home crowd, Leeds started positively and won a free-kick high up the pitch when Joe Rodon strode forward from centre-back.
Angus Gunn was evidently expecting a delivery into the area from Crysencio Summerville, but an inventive effort from Ilia Gruev caught the shot-stopper flat-footed as he whipped in his first goal for Leeds.
Daniel Farke’s side had taken the lead in 22 league games this season, coming out on top on 20 occasions - a concerning statistic for a trailing Norwich side that soon found themselves two goals down when Joel Piroe nodded in Wilfried Gnonto’s superb cross at the back post.
A fine one-on-one stop from Illan Meslier denied Josh Sargent soon after and kept the momentum with the hosts, who added a third before half-time with an empathic Georginio Rutter strike that cannoned in off the underside of the crossbar following a swift breakaway.
Norwich were perhaps fortunate not to be further behind after a late first-half flurry, which seemingly continued straight after the restart as Piroe twice forced close-range stops from Gunn.
Having guided the Canaries to two Premier League promotions in his time at Carrow Road, Farke watched on as his current side cut through the visitors once more, extending their lead through Summerville, who tucked in Junior Firpo’s cut-back with over 20 minutes still to play.
A forlorn David Wagner could do little to change the outcome in the closing stages, with his late alterations ultimately proving inconsequential.
As such, a third consecutive defeat at Elland Road means the Canaries will spend a third successive season in the second tier.
Meanwhile, victory for Leeds against either Southampton or West Bromwich Albion in the Championship play-off final would mark the 10th time in 20 years that the third-placed side have gone up.
After five previous unsuccessful EFL play-off promotion campaigns, it may well be sixth time lucky for the favourites, who would join Leicester City and Ipswich Town in the top flight.
Flashscore Man of the Match: Georginio Rutter (Leeds)