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Goalkeeper Arthur Okonkwo was the hero for the hosts, saving Forest's fifth penalty by Omari Hutchinson to ensure the win.

"It was amazing to win the game in the end. We just have to enjoy the moment," Okonkwo said after his heroics.

Wrexham's Liberato Cacace and Oliver Rathbone scored in quick succession in the first half. The second-tier team looked headed for victory with a 3-1 lead in a breathless second half before Callum Hudson-Odoi struck in the 76th and 89th minutes.

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Forest boss Sean Dyche had selected a virtual reserve team with eight changes from the midweek Premier League win over West Ham United.

But he sent on reinforcements in Neco Williams, Nicolas Dominguez, and Morgan Gibbs-White for the second half, and it paid off as Igor Jesus pulled one back in the 64th minute, nodding in a cross off the post.

Dominic Hyam restored Wrexham's two-goal advantage when he dove to head home a free-kick in the 74th minute before Hudson-Odoi's heroics.

But Wrexham prevailed in the shootout after extra-time ended without a goal and the victory was another highlight for a team that has climbed from non-League football to the second tier in three consecutive seasons under the ownership of Hollywood A-listers Ryan Reynolds and Rob McElhenney.

Canadian Reynolds was at the game.

"The lads rallied themselves, and there were a lot of tired legs on both teams. Credit to both sides for putting on such a good game after such a busy Christmas schedule," Wrexham boss Phil Parkinson said.

An angry Dyche gave a scathing review of his starters.

"The first half was completely unacceptable," he said. "I let the players know this. Certain individuals certainly know. They will have to look in the mirror.

"But, the strangeness of football, the players who came on in the second half I think were a credit. We went on and looked like a Premier League side.

"But you can't do that in the first half. It's one of them, they all knock on your door and say, 'Why aren't I playing?' Well, the evidence was quite honestly there for some, not for all."

Elsewhere, Championship side Oxford United beat EFL League Two's MK Dons on penalties after their match ended 1-1, while a couple of EFL League One teams moved on, with Wigan Athletic beating Championship side Preston North End 1-0, and Port Vale defeating League Two's Fleetwood Town 1-0.

Holder Crystal Palace heads to non-league Macclesfield Town, the lowest-ranked team remaining in the competition, in one of the 18 games to be played on Sunday (AEDT).