Kieffer Moore celebrates after scoring the fourth goal of the game in the clash with the Blades.
The Welsh international scored twice as Phil Parkinson's side mounted a remarkable fightback from a two-goal deficit to defeat his former club Chris Wilder's men in a pulsating 5-3 second-tier encounter.
The forward's excellent first-time shot put United ahead, but Wrexham levelled almost immediately thanks to a Tyler Bindon unfortunate deflection.
Bamford's second and a Callum O'Hare nod appeared to have put the visitors in command at 3-1, before the towering striker pulled one back with a thumping header of his own.
The winger's header early in the second half brought the scores level, paving the way for the goalscorer to give his side the lead for the first time with 14 minutes left to play.
The midfielder's composed spot-kick in the closing stages wrapped up the points, halting a sequence of five games without a win for the Welsh club.
When these two sides met in the FA Cup back in 2023, it ended in a epic 3-3 draw.
Friday's encounter provided a further epic, breathless installment in their growing rivalry.
With the support of Hollywood owners, Wrexham's meteoric rise through the leagues has brought them back to the Championship for the first time in 43 years.
Ahead of this fixture on the back of a winless run, the boss had demanded a replication of the characteristic fighting qualities from those past encounters.
His team certainly delivered, overcoming a two-goal hole to claim a memorable 5-3 victory that highlights their resilient attitude.
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