Cardiff dominated possession from the outset, although it was Nathan Broadhead who had the best opening early on as he drilled wide.

But the home side’s slow start was encapsulated when George Thomason was robbed of possession in the 13th minute. Rubin Colwill capitalised and picked out Kellyman whose shot was superbly saved by Burton, although Salech was on hand to tap home the rebound.

It will have been hugely pleasing for Bluebirds boss Brian Barry-Murphy, whose side saw plenty of the ball at Bolton Wanderers on Saturday but conceded in added time to lose 1-0 and end the game without a single shot on target.

Wrexham had goalkeeper Burton to thank for keeping their side’s deficit at just one goal as he denied Kellyman at his near post, before tipping Ashford’s thumping hit on to the crossbar.

The frame of the Wrexham goal then came to the home side’s rescue as Rubin Colwill’s free-kick rattled the crossbar, causing the Wrexham faithful to grow increasingly restless.

The Red Dragons eventually showed signs of life shortly before the break, although Sam Smith drilled a low shot wide from distance to leave the hosts with an uphill battle in the second half.

Phil Parkinson responded with a triple substitution at the break – with Moore, Josh Windass and Matty James replacing Smith, Broadhead and Ollie Rathbone.

And Wrexham levelled proceedings seven minutes into the second half as Ryan Longman’s deflected cross from the left was was met by the onrushing Moore, who headed beyond Nathan Trott from close range for his sixth goal of the season.

The game was far more even by this point, and shortly after Rubin Colwill fired straight at Burton.

Barry-Murphy sent Alex Robertson and David Turnbull on for Ryan Wintle and Joel Colwill, having earlier summoned Isaak Davies from the bench.

Just two minutes after coming on, Robertson forced Conor Coady into a crucial block, but Cardiff retook the lead in sublime fashion soon after.

Joel Bagan’s deep cross found Fish unmarked at the back post, and the 22-year-old volleyed beyond Burton at the near post to bag his first goal for the club in spectacular fashion – sparking wild scenes of celebration among the 1,249 fans in the away end.

Parkinson’s final roll of the dice saw Issa Kabore and Ryan Hardie replace Coady and Ryan Barnett.

Hardie’s first touch was to head Lewis O’Brien’s free-kick straight at Trott, and less than a minute later, the Scot had a shot blocked after going through on goal.

At the other end, Burton got enough of a touch to keep out Isaak Davies’ fierce strike.

But Wrexham were unable to find a late equaliser to send the tie to a penalty shootout, as Cardiff progressed into the last eight for the first time since reaching the final during the 2011-12 season.