After as rambunctious a play-off second leg as can possibly be imagined Derby claimed the right to face Aston Villa in the final on 27 May to try for promotion to the Premier League. It was end-to-end entertainment all night, a feast of incident, goals and excitement, and neither side – both reduced to 10 men – deserved to lose.

It never ceases to astonish how full-blooded and thrilling play-offs can be, when both sides must know the likely prize on offer, financial considerations aside, will be a season of toil and tribulation in the top flight. Dreams shattered, Leeds players hit the deck in the manner of Ajax a week ago as the final whistle sounded. They had been true to Marcelo Bielsa’s attacking traditions but let themselves down in defence on a couple of occasions. Frank Lampard now has a shot at the big time at the end of his first season as manager.

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Lampard said beforehand that Derby’s first task would be to quieten the Elland Road crowd and though the ground was at its most raucous at kick-off the visitors were not doing a bad job of quelling the atmosphere until Stuart Dallas gave the home side the lead midway through the first half.

Leeds had started brightly before being pushed back and were struggling to get the ball into the Derby box before they were awarded a free-kick 30 yards out. Kalvin Phillips flighted it perfectly and though the ball may not have made any contact with Patrick Bamford’s forehead the striker proved a distraction. Kelle Roos could not prevent the cross striking an upright and Dallas tucked away the rebound.

Facebook Twitter Pinterest Frank Lampard leads the Derby celebrations. Photograph: Alex Livesey/Getty Images

With a 2-0 aggregate deficit Lampard’s strategy had no chance of succeeding, and aAs the Leeds fans turned up the volume there were some predictable taunts at the Derby manager and his Chelsea background. Events were quite feisty on the pitch as well, with Scott Malone and Pablo Hernández booked after a touchline clash, Phillips picking up a card for a poor challenge on Harry Wilson and Bamford being given a yellow for simulation in the Derby area.

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Leeds were making good progress down the right wing with Hernández and Mateusz Klich finding space, and a cross from the latter might have broken the deadlock even earlier had not Luke Ayling put his volley over the bar. Mason Bennett hit the post with a looping header a couple of minutes before the interval, yet though that indicated Derby were still capable of getting back on terms the manner in which they did so surprised everyone.

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First Lampard made an enforced substitution in the 44th minute, sending on Jack Marriott for the struggling Duane Holmes. Marriott trotted on to the pitch probably expected a kick or two at best before the half-time whistle, but immediately found himself the beneficiary of a mix-up between the Leeds goalkeeper, Kiko Casilla, and the centre-back Liam Cooper when trying to deal with a loose ball.

Casilla came out of his area then retreated, leaving Cooper to hurriedly attempt to clear, and the ball squirted between the two of them to leave Marriott to find an open goal with his first touch. It was not the conclusion to the first half Leeds wanted, and when Casilla managed to leave his area again before half-time without properly giving Gaetano Berardi time to clear there were audible grumbles from the fans behind his goal.

Facebook Twitter Pinterest Gaetano Berardi lunges at Bradley Johnson for a second yellow card that proved to be a turning point in the tie. Photograph: Nick Potts/PA

Plenty has been written in the last few days about the role momentum and confidence play in comebacks and Derby needed less than a minute of the second half to offer the latest evidence. Completely undaunted by the rousing rendition of Marching On Together that greeted the resumption of play Richard Keogh drove forward to find Mason Mount, who made room inside the area for a shot and scored only 38 seconds after the restart. He somehow produced an effort on target despite appearing to stumble in the attempt. Tellingly that was Derby’s second attempt on target of the evening, yet both had produced goals.

Leeds tried frantically to regain the lead, only to come up against some inspired Derby defending. Jayden Bogle cleared off the line from Phillips, Roos stood up to a fierce shot and when a follow-up came in at even greater velocity Malone bravely stuck his face in the way.

The force was with Derby and the next time they went upfield they scored. Cooper received a booking for tugging Bennett’s shirt in the area and Wilson calmly stroked in the penalty. That made it 3-1 on the night and put Derby in front in the tie for the first time but they could hold on to the advantage for only five minutes.

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Dallas took a neat return pass from Klich to burst into the area and beat Roos with a firmly struck low shot for his second goal.

Emotions were still running high and Berardi’s temper got the better of him as he was goaded into retaliation in the 78th minute to pick up a second yellow nine minutes after his first. The right-back punched the extendable tunnel in frustration as he left the pitch and Leeds had to see out the remainder of the game with 10 men.

Bogle had a penalty appeal turned down, Wilson struck a post when he really should have scored but finally, with five minutes left, Marriott closed the second half as he had ended the first, with a well-taken goal after Keogh won the ball to start the move and then produced the decisive pass to Marriott.

Malone earned a late dismissal for a second yellow, while Isiah Brown and Jack Clarke tested Roos in the closing seconds but the goalkeeper stood firm to leave Leeds on the floor.

• This article was amended on 17 May 2019 to remove an incorrect reference to “Roos stood up to a fierce shot from Bradley Johnson”. Johnson plays for Derby.