The Red Dragons are unbeaten in all eight of their FA Cup ties played at Stok Cae Ras under their current manager - winning six outright, progressing via a subsequent penalty shoot-out in another and earning a replay from the other.
But they will have to be at their rip-roaring best as they welcome Premier League Chelsea to north Wales on Saturday evening.
Having already dumped out a top-flight side in Nottingham Forest and promotion-chasing Ipswich Town in this season's run to the fifth round, Wrexham will have every faith that they can cause yet another upset in the world's oldest national football competition.
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And Parkinson's men go into the contest in fine fettle.
Their gritty 1-0 win at Charlton Athletic last time out was their third league triumph in succession, the second time this season they have managed that feat in the Championship.
They have shown a range of different qualities during the course of their league wins against Ipswich, Portsmouth and Charlton in the week prior to the visit of Liam Rosenior's Blues.
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There was courage, quality and spirit to come from 3-2 down to beat the Tractor Boys 5-3 in an absolute thriller.
That was followed by an incredibly strong attacking showing in the first-half against Pompey, and a solid rearguard effort in the second-half.
As for the win at The Valley, Wrexham certainly rode their luck and were perhaps fortunate to leave the English capital with all three points.
But even opposition boss Nathan Jones was gracious enough to acknowledge that Wrexham's ability to grind out victories is admirable.
"Good sides find ways to win games, that's what they've done – and they are a good side," said the Welshman.
"You don't win the games they have in a four-year period if you are not."
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In reaching the FA Cup fifth round, Wrexham have already earned £127,000 in prize money, a sum that will increase to £238,500 if they can upset the odds to beat eight-time winners Chelsea.
Then, of course, there is the broadcast revenue they will generate from having the match screened live on TV around the world, in addition to the gate receipts.
But Wrexham's prime focus this season, particularly now with such a daunting task ahead of them in the FA Cup, simply has to remain on gaining promotion into the Premier League.
They currently have a four-point buffer over seventh-placed Southampton and are guaranteed to remain in the play-off places after their encounter with Chelsea, even without playing a Championship match this weekend.
And while the prospect of securing a monumental scalp against Chelsea remains a tantalising one, Parkinson's decision to call the cup tie a "bonus" spoke volumes - not that he will be taking it lightly, of course.
"We said to the lads that the Chelsea game was a huge bonus, a high-profile game, but there was a determination about us to go into it with a good performance," he said after the triumph over Charlton.
"Now, it’s a deep breath and let the lads relax a bit and get ready for what will be a terrific night for the football club next Saturday."
It all means Wrexham can go into the game adopting a win-win mentality, as their match-up with Chelsea represents a true free hit.
Parkinson's side can be thrilled with the way they have gone about their business this season, and, whatever the outcome against the Blues, those in red and white can rest assured that they still have a huge amount to play for after Saturday's game has been and gone.
