A flying start to their Premier League season had seen David Moyes' third-placed side installed as one of the frontrunners to lift this trophy, but Aidy White's fourth-minute goal and Rodolph Austin's effort with 20 minutes left saw Leeds through, despite a nervy ending prompted by Sylvain Distin's header on Tuesday night.
The performance of Austin - a Jamaica international who has spent most of his career in Norway - was at the centre of Leeds' victory, with the midfielder coming out on top of his battle with another man mountain, Marouane Fellaini.
The Belgium international was one of just five Everton players to retain his shirt from Saturday's 3-0 win at Swansea in what was a first meeting between these two sides since April 2004, when the goals in a 1-1 draw were scored by James Milner and Wayne Rooney.
Everton have remained a stable top-flight force since then while Leeds have dodged from one false dawn to another in their bid to return to it. The Bahraini businessmen watching on Tuesday night who are in talks with the club over investment may well fancy their chances of making that happen.
For Everton, though, despite their strong league start, their best chance of a trophy this season has now passed them by, with Moyes unable to summon enough from a well-stocked bench to put Leeds off their stride.
While the Scot may have tinkered with his side he was careful to ensure he had the experience of Distin, Fellaini, Johnny Heitinga and Steven Naismith on from the off, but three of that quartet were left red-faced early on as White got Leeds off to the perfect start.
Sloppy passing from Naismith and Coleman sold debutant Francisco Junior short and, after he had been mugged by Austin, the ball found its way to White who skipped past a token challenge from Fellaini. With cover nowhere to be seen he took aim from just inside the area and left Jan Mucha grabbing the air with his first goal for United.
Everton's response was muted and it took until 28 minutes for them to get a genuine sight of goal, and when it came Victor Anichebe hit a rising ball over after Bryan Oviedo had gone down the right and played him in.
That was Everton's last contribution of the half and they were fortunate not to be 2-0 down when referee Lee Mason brought it to an end.
First Luciano Becchio and El-Hadji Diouf combined to play in White, whose low shot was well pouched by Mucha on a wet pitch. Then, in injury time, Becchio wasted a golden chance when he headed a Diouf cross at the only place in the goal where Mucha could have stopped it, with Naismith clearing up the loose ball on the line.
Moyes beckoned Phil Neville and Steven Pienaar from the bench at the break and the latter powered a good chance over the bar nine minutes later, picking up Jason Pearce's clearance but failing to hit the target.
Everton had clearly upped the ante but Leeds were not without chances either as Michael Tonge slipped into the box and saw his curling effort drift away from Mucha's far post.
Neither of those chances were as good as the one presented to Naismith on the hour, though, with the forward heading Anichebe's cross wide when unopposed, two yards out at the back post.
Anichebe then whistled a low drive just away from goal and soon after Nikica Jelavic was sent on as Everton's last throw of the dice, but a Leeds spell of pressure followed and unlike Everton they topped it with a goal.
Austin's weaving run was halted by Coleman on the byline and from the subsequent free-kick, Diouf pulled back for Danny Pugh, whose goalbound effort was turned in by Austin.
Everton managed to scramble a reply when Distin headed in with 10 minutes left after some slack marking from Leeds, and thought they had a shot for a penalty when Pearce and Anichebe tussled, but United held on.