The victory was the Cards' first in six Conference outings, while the home side have now picked up just one point from their last three games.
Midfielder Murray gave the visitors a perfect start with just eight minutes on the clock as his well-placed shot beat home keeper Danny Potter.
Kezie Ibe and Lee Boylan tested Cards keeper Shwan Jalal as the Islanders hit back, but eight minutes before the interval Woking doubled their lead.
Potter made a fine save from Gary MacDonald following a Liam Cockerill corner, but from the resulting flag-kick Tom Hutchison's flick-on allowed Ferguson to steer the ball home from close range.
Jalal made an excellent save to deny Boylan from a 25-yard free-kick just before half-time and soon after the restart he tipped over a Mario Noto effort.
The home side continued to press for much of the second period without looking like breaking through and getting back in the game.
Jalal made further saves from Ibe, Boylan and Dwain Clarke to make sure of a well-earned clean sheet for Glenn Cockerill's mid-table outfit.