Paul Mullin looked as though he sealed a dramatic second half comeback against Sheffield United, only to be denied at the death by John Egan, sending the contest to a replay.
The visitors got off to the dream start, as Ollie McBurnie nodded home from the first corner of the match.
Wrexham were dealt two further blows, losing Jordan Tunnicliffe and Aaron Hayden to injuries inside the first ten minutes.
The hosts held were in the driving seat at the break, but the Red Dragons put their foot on the gas at the start of the second, with James Jones levelling and Tom O’Connor heading into the lead.
Oliver Norwood put the game back on level terms in the 66th minute, but the pendulum swung back in the host's favour, as Daniel Jebbison received a red card five minutes later.
It looked as though Mullin won the game in the 86th minute, but Egan had the final say, taking the game to a replay.
Phil Parkinson named an unchanged eleven from the side that moved to the top of the National League on Tuesday night.
However, the high-flying Championship opponents made five changes, as the Blades looked to make it 10 unbeaten.
They started the game in fine fashion too, as McBurnie arrived unmarked inside the penalty and headed past Howard.
In the immediate aftermath of the goal, Jordan Tunnicliffe was substituted after receiving a lengthy period of treatment.
Things got harder for Wrexham as Aaron Hayden was substituted on the ten-minute mark, with what seemed like an innocuous injury.
However the response was a positive one and there could have been a penalty for the Red Dragons when Mullin chased down Forde’s through ball, and he went down after being caught by Davies.
The Blades looked to double the advantage, as Daniel Jebbison advanced on goal but Mark Howard was out to make a crucial save.
He was called into action again on the 20th-minute mark, as Jayden Bogle launched a speculative effort from range, but Howard was more than equal to it as he parried it away.
Despite a flurry of chances from United, Wrexham grew into the game and Elliot Lee struck a sweet first-time volley that looked destined for goal, but Basham made the all-important block.
With the early injuries and substitutions, the referee awarded seven minutes of additional time as Parkinson’s men looked to get back in the game.
The final chances of the half both fell to Paul Mullin and the first a rasping driven effort which forced Davies into parrying.
The other, a free kick which was blocked by the well-marshaled Blades wall.
The second period got off to a flyer, Luke Young had a dipping strike spilled by Davies and they somehow survived the resulting goalmouth scramble.
Their luck ran out quickly and James Jones levelled in the 50th minute, as the ball bounced around the six-yard box from the Tozer throw, and he converted past Davies.
The pressure started to mount on the Championship outfit, with Wrexham creating chances, and they soon found themselves behind.
Young’s corner found its way to O’Connor arriving at the near post and he slotted home cooly, with none of the Blades backline picking him up.
The game continued to ebb and flow, and Ollie Norwood did well to break away, and after Tozer’s goal-line clearance, the striker poked home the rebound.
Just as the Blades got on level terms, Heckingbottom’s men were dealt a blow, when Jebbison received a straight red after an off-the-ball incident.
The ten-man side found themselves under the cosh and was made to pay in the 86th minute, when Mullin slammed the ball past Davies, sending Wrexham fans into raptures behind the goal.
However, there was to be one final sting to the tail, as Egan rose at the back post in the fifth minute of added time, sending the tie to a replay.
Wrexham: Howard, Forde, Hayden (Cleworth 5’), Tozer, Tunnicliffe (J.Jones 9’), McFadzean (Dalby 75’), O’Connor, Young ©, Lee, Mullin, Palmer
Yellow Card: Young (56’), McFadzean (64’), Tozer (71’)
Subs not used: Lainton, McAlinden, Lennon, Bickerstaff, Cannon, Hall-Johnson
Sheffield United: Davies, Ahmedhodzic (Coulibaly (87’), Egan, Basham, Bogle, McAtee (Lowe 46’), Norwood, Doyle, Osborn (Ndiaye 58’), Jebbison, McBurnie (Sharp 58’)
Yellow Card: Egan (45 +7), Bogle (90+1)
Red Card: Jebbison (71)
Attendance: 9909 (1163 away)