In-form Cards striker Scott Rendell notched his seventh goal of the season in stunning fashion with a 30-yard pile-driver (24) against the run of play, but Wrexham levelled through a consummate Louis Moult finish (38).
Dean Morgan (66) regained the lead for the visitors with his third chance in as many minutes and it could have been worse had the cross-bar not come to Wrexham's rescue.
An assistant linesman's flag ruled out what Moult thought was his second goal but the leveller failed to materialise as Wrexham failed to add to their solitary Racecourse win in four attempts this season.
Wilkin made three changes to the side that took to the field in the 2-2 Bank Holiday Monday draw against Macclesfield Town.
Andy Coughlin paid for the error which led to the Silkmen's opener with Wilkin recalling on-loan Stoke City custodian Dan Bachmann.
Penycae's Rob Evans was handed his first start of the campaign, replacing the injured Jay Harris whilst Ross White was pitched into his first senior Wrexham action with Mark Carrington benched.
Wrexham got off to what Wilkin and the home faithful hope is becoming a customary quick start -Wes York running straight at the defence from the kick-off.
Wrexham's early dominance was almost rewarded in the 10th minute but Cards stopper Aaron Howe tipped over a mischievous 20-yard shot from Connor Jennings.
He then denied White a goal on his debut, palming his header around the post as Wrexham racked up the corners.
But a sense of déjà vu spread around the Racecourse when Woking took the lead against the run if play.
Rendell, who hit a four-goal salvo in his side's 6-1 demolition of Dover Athletic, showed deadly accuracy with a stunning shot from all of 30 yards which arrowed past Bachmann.
It briefly knocked Wrexham out of stride before they restored parity seven minutes before the break.
Elliott Durrell put the ball into Moult's path and the striker was coolness personified as he stroked the ball low past Howe for his third goal in four games.
Dean Morgan and Jennings enjoyed chances at either end as the second half opened up on a rain-lashed surface.
Morgan volleyed straight at Bachmann and Wrexham failed to heed the warning signs as the tricky winger slotted home after finally getting the better of White.
James Clarke missed a golden chance to settle matters but his hooked shot crashed against the underside of the bar, whilst Bachmann smothered a low drive from Kieran Murtagh as Wrexham wobbled.
Moult picked up a booking as frustrations grew before Reds boss Wilkin threw on Andy Bishop and Theo Bailey-Jones.
Moult thought he'd levelled again only for an offside decision to cut short his celebrations.
Wrexham pressed late on but Woking held firm to continue their impressive start to the campaign.
Wrexham: Bachmann: Ashton (cpt), Smith, Hudson, Clarke, Durrell (Bishop, 76), Moult, Evans, York (Bailey-Jones 76), White (Carrington, 82), Jennings.
Subs: Coughlin, Stephens.
Referee: Ian Hussin
Wrexham: Ashton,Moult, Clarke