The Fleet, with only eight points from a possible 42 since losing leading scorer Charlie MacDonald to injury, were desperate for a win to ignite a season fast developing into a damp squib.
Both sides were reduced to ten men in the 12th minute when referee Bull showed straight red cards to Fleet skipper Paul McCarthy and Woking's Steve Ferguson.
McCarthy had clattered into Ferguson, who responded by slapping the defender in the face, setting off a violent response. With a three-match ban looming, the dismissal signals the end of McCarthy's Conference season.
Auxiliary striker James Smith dropped back to defence to cover for McCarthy's absence, further diluting the Fleet's attacking options.
Woking, bound for the FA Trophy Final, had far more firepower on offer with Craig McAllister partnering Justin Richards, but they made hard work of supplying ammunition to their strikeforce.
Moore had a good chance to put Gravesend in front midway through the first half when he connected with Andy Drury's cross from the left wing, but Shwan Jalal made an excellent save to turn the ball away for a corner.
Woking responded through Karl Murray, who shook off James Smith's challenge in the Fleet area but could only fire high over the bar.
Back came the Fleet and Drury dragged his shot wide of a post after good work by Danny Slatter.
Gravesend took the lead with virtually the last kick of the first half. With two minutes added on, Drury's corner fell to Johnson on the far side of the penalty area and the midfielder, on loan from Northampton, rifled his left-foot shot into the net past a despairing Jalal.
With his side treading water, Glenn Cockerill made a double substitution midway through the second half, Neil Smith and Malik Buari replacing McAllister and Shola Oyedele, but the Cards seemed resigned to their fate and barely flickered into life in the remainder of the game.
Buari force a reflex save from Craig Holloway but it was the Fleet who found the back of the net on 76 minutes.
Johnson placed a great ball through to Moore and the youngster outpaced the flat footed visitors' defence to blast the ball into the roof of the net.