Wrexham denied Hollywood ending in dramatic FA Cup thriller
Reynolds and fellow actor Rob McElhenney took over the National League side in 2020.
The American celebrated the Welsh club's three goals wildly in the stands, but they will need to win a replay to reach the last 16 of the FA Cup for the first time since 1997.
Wrexham could not have got off to a worse start as Oli McBurnie headed the Blades in front after 61 seconds.
Sheffield United look set for a return to the Premier League next season but they were rocked by a pulsating atmosphere inside the Racecourse Ground.
The home side struck twice in 11 minutes early in the second half to turn the tie around as James Jones and Thomas O'Connor scored from set-pieces.
Oli Norwood looked to have ended the Wrexham dream with a composed finish to equalise.
But a red card for Daniel Jebbison for an off-the-ball incident handed the hosts 20 minutes with an extra man to find the winner.
They seemed set for a Hollywood ending when top scorer Paul Mullin steered home in the 86th minute.
However, there was a final late twist in the plot as John Egan forced home a corner in the 95th minute to force a replay.
Mullin said he was "very disappointed" to concede so near the end of the match.
"If we just hold on against 10 men then we are through," he told the BBC.
"I thought we were the better team throughout the game, creating chances and looking dangerous on the break. We limited them to not many chances in open play.
"I'm so proud of everyone. We've worked so hard to get here. We came into the game thinking we could win and we had a game plan. Unfortunately it hasn't quite paid off but I think when the dust settles tomorrow we'll be proud of it."