The Cards made a perfect start in just the second minute of the game, leading scorer Justin Richards played the ball in from the right and Craig McAllister slotted the ball past Ryan Clarke.
Clarke's day got even worse with 11 minutes on the clock as he was red-carded for a deliberate handball outside his penalty area.
Ryan Harrison came on as a replacement, with Scott Rogers the man to make way, with Karl Murray compounding the misery by firing home the resulting free-kick to double Woking's lead.
Bruno Teixeira almost got a goal back for Rovers, but Richards made it 3-0 on the half hour, taking his season's tally to nine with a crisp finish.
Shortly after the restart, Harrison made a smart save from Steve Ferguson, while Teixeira tested visiting keeper Shwan Jalal on the hour.
Rovers could find no way back into the game and Ferguson was again denied by Harrison five minutes from time.