It was left to the Grecians to do all the work as the visitors sat back for a point but they ultimately proved impossible to break down.
Striker Jake Edwards had the best chances for Exeter with a couple of close-range shots while Gary Sawyer and Gareth Sheldon also went close.
Exeter enjoyed plenty of possession in the opening period but were unable to convert it into chances.
Edwards had an early chance for City when he headed Les Afful's corner just over the bar.
Lee Phillips, preferred in attack to veterans Steve Flack and Sean Devine, met Scott Hiley's cross but headed into the arms of the goalkeeper.
Afful twice fired over the bar after being found inside the box as Exeter began to dominate.
The best chance of the first period fell on the stroke of half-time. Sawyer's deep cross fell to Edwards after goalkeeper Shwan Jalal slipped, but his close-range effort was scrambled off the line.
After the break Woking attempted to push forward and Louis Jefferson's snap shot flew over the bar.
Edwards struck a shot narrowly wide from close range for Exeter after a fine run from the lively Afful.
Afful then forced Jalal to save well with a low strike form 12 yards. But it was a frustrating afternoon as Exeter failed to turn their possession into chances.
Veteran strikers Devine and Flack were introduced for the Grecians as they desperately sought a winner.
Substitute Sheldon almost opened the scoring with his first touch with a right-foot volley which was superbly saved by Jalal.
Devine thought he had given Exeter the lead with two minutes left on the clock, but his effort was rightly ruled out for an obvious handball.
In injury-time Sawyer volleyed a shot over the bar but there was no way through for Exeter.