On-loan winger Tony Scully struck his second goal of the season to put the home side in control with a well-taken header.
But Karl Murray spoiled the party by lashing home a magnificent free-kick to continue Woking's recent momentum.
Exeter City, the early pace-setters in the Nationwide Conference, came into the game on the back of two defeats at the hands of Stevenage and Burton Albion.
But once again hopes of grabbing all three points disappeared as they allowed their visitors a route back into the match.
It was the home side that fashioned the clearer chances in a pulsating first half. Andy Taylor lashed a free-kick over the bar, Lee Phillips was denied by Shwan Jalal before the home side broke the deadlock.
Scully latched onto a long throw from Jon Challinor to head home after 27 minutes.
The hosts came close to stretching the lead with Scully, Leslie Afful and Phillips all wasting decent opportunities.
But Woking gradually forced their way back into the contest after the break and Steve Ferguson was foiled by keeper Paul Jones just 48 seconds into the second period.
Woking finally grabbed an equaliser when Murray curled an exquisite free-kick into the bottom corner of the net.
The bombshell prompted City to go in search of a winner and Billy Jones lofted a free-kick inches past the post.
With time running out, Craig Farrell came within a whisker of sealing all three points, but his looping effort dipped over the bar.