York City began the first half on the front foot, with the better chances, but couldn't force an opener against the Cards.
It was just before the hour mark when they did manage the break the deadlock, through a free kick, which was headed in by Sam Sanders.
While Woking dominated the opportunities in the second half, Lenell John-Lewis sealed the game for the visitors in the last minute, slotting home on the counter-attack.
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Story of the match
For the first game under new management at York City, it was assistant Michael Morton who took charge, and made just two changes from last week's draw with Wrexham, as Sam Sanders came in to replace Adam Crookes in defence, plus Gus Mafuta dropped out for Luke James.
Darren Sarll made four alterations to his Woking side, as Dan Moss, Jake Vokins, James Daly and Jack Roles all returned to the starting lineup.
As they did in the reverse fixture against the Cards, York started on the front foot, with Luke James latching onto a long ball after only four minutes, his fierce half-volley hitting the side netting.
Entertaining isn't a word that many would have chosen to describe the first 20 minutes - the possession was mostly dominated by Woking, but it was the visitors who had had the best chance early on, and a deflected effort onto the roof of the net almost troubled their opponents again.
That seemed to be enough of a warning sign for the Cards, who came close for the first time of the afternoon, James Daly seeing a shot from the left roll narrowly across the face of goal.
Six minutes shy of half time, York had yet another golden chance to net the opener, a lofted cross from Lenell John-Lewis finding right-back Michael Duckworth at the far post, but he just couldn't direct his header on target.
That concluded the first half, with the Minstermen no doubt the most likely to grab an opener, though a Darren Sarll team talk didn't change much for the second half.
A few nervy moments were forced on City by the Surrey outfit, including a tame Scott Cuthbert header, but nothing bothered 'keeper Ethan Ross.
59 minutes in, and the game was in desperate need of a goal to liven things up - that was when York made a set-piece count. Substitute Nathan Thomas swung in a free-kick from the left of the goal, and an awkward header from a Cards man took it to the back post, for defender Sam Sanders to nod home for his third of the campaign, and to give the visitors a deserved lead.
Just four minutes later, things went from good to bad for the Minstermen, when a through-on-goal Rhys Browne was wiped out by centre-half Fraser Kerr. The potentially goal-preventing challenge wasn't a particularly legal one, and Kerr was rightly punished with a straight red card.
Unlike his defensive partner, Sanders retained his 'hero' status in the game, proving his excellence at both ends of the pitch, putting in a crucial block to deny a goalbound Jermaine Anderson strike from the edge of the box.
With Woking still trailing for 10 minutes, a good corner delivery almost found them a leveller, but Joe McNerney couldn't keep his header down from drifting over the bar.
The chances kept on coming for the hosts, as Padraig Amond burst forward into the box, and after doing practically everything right, he dinked it over Ethan Ross, only to watch his effort come back off the face of the post.
In the midst of countless chances for the Cards, midfield master Dan Pybus had the ball fall to him 20 yards from goal, but his hopeful first-time strike looped inches over the top-right corner.
Then, with one minute left of the 90, a City break saw John-Lewis through on goal, and with just the 'keeper to beat, he made no mistake in slotting home to double his side's lead, and send the travelling faithful into elation.
A sizeable nine minutes of added time didn't receive the most pleasing response from a certain section of the ground, but it gave the hosts marginal hope of finding a way back.
Masses of tactical time-wasting from York didn't help their opponents' situation, but they did get one more chance, deep into injury time. Amond put everything into his fierce strike, which looked to be heading for goal, but only for it be be brilliantly tipped over by Ross, a final attempt to keep a clean sheet.
A first three points for the Minstermen since October moves them up to 15th, while Woking, who will feel hard done by, having had the double done over them, drop down to 4th.
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Player of the match
Sam Sanders (York City)
