Dani Ceballos netted in the 91st minute to give Arsenal hopes of a silverware and qualification into the FA semi-final in one of the under performance of the season.
Ceballos who is on loan in London sent a low finish to hand Arsenal the deserved win of the night after the host equalized deep in the second half.
The visitors took the lead in the 25th minute when Nicolas Pepe converted from the spot when Alexandre Lacazette was brought down in the penalty box Chris Basham.
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Arteta survived an early first half scare when John Lundstram header was ruled for an offside in the eighth minute of the match.
Sheffield United were again ruled out for an offside when McGoldrick found himself past the last defender.
David Luiz who was coming from a red card suspension limped out in the 54th minute with an injury and replaced by Rob Holding.
Tittle hopes for arsenal
The win gives Arsenal coach Mikel Arteta an opportunity to turn around fortunes since the failed reign of Unai Emery.
It will also bring back the competitive edge set by former coach Arsene Wenger in a club that last lifted the cup in 2017.
Trailing in 9th position and no hopes for a top five finish, winning the cup gives them an opportunity to bounce back in Europe.