They will now turn their attention back to the quest for promotion to the top flight while for Clough – whose father Brian won the League Cup on four occasions – and his players, the unlikely dream goes on.

The unmarked Jordan Hugill came within inches of putting the home side ahead when he only just failed to reach Martin Braithwaite's sixth-minute cross from Dael Fry's intelligent through-ball and then looped a header on to the roof of the net.

Burton keeper Bradley Collins had to produce a fine reaction save to deny Lewis Wing, whose piledriver against Premier League Crystal Palace had handed the Teessiders their place in the last eight, after he had been played in by Stewart Downing with Boro working their way into the ascendancy.

The visitors tested keeper Darren Randolph for the first time, although not to any great extent, when defender Ben Turner got his head to Scott Fraser's back-post cross, but opposite number Collins needed to be alert to to claw away Downing's 28th-minute free-kick.

Stephen Quinn lifted a snapshot over the bar 12 minutes before the break as the Brewers responded, but both Collins and Jake Buxton had to block efforts from Hugill in quick succession after he had been played in over the top by Muhamed Besic.

But Harness might have handed Burton the lead in stoppage time after Hesketh had stepped over Lucas Akins' cross, only for the winger to sidefoot wastefully over.

Tony Pulis' men made an untidy start tot he second half, and were made to pay within three minutes when, after Fry had given the ball away, Fraser played in Jamie Allen and although his shot came back off the far post, Hesketh rifled the rebound past the diving Randolph.

Boro were in disarray and might have fallen further behind within four minutes when Harness show a shot deflected over the bar and with a fightback failing to materialise, the manager made his move when he sent on Marcus Tavernier and Britt Assombalonga for Besic and Hugill with 27 minutes remaining.

But the home side were simply unable to summon up the quality they needed to rescue themselves with Flint somehow heading Tavernier's cross wide at the death on a famous night for the men from the Pirelli Stadium.

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