Matchwinner Zdrilic sealed the game with his 75th minute goal but the Aussie had previously failed to make much impact before his important strike.
Walsall had every reason to be indebted to goalkeeper Jimmy Walker in a goalless first half. Walker, who handed three points on a plate to Wolves in the previous home game, kept the Saddlers in contention with a brilliant save to keep out a powerful drive from Neil Shipperley.
Wimbledon's leading marksman, who had previously been kept in tight check by Danny Hay, ploughed through the mud to fire in his first shot on target only to see Walker dive to left to push the ball away for a corner.
Following such a disappointing first half Wimbledon sent on Gareth Ainsworth in place of Patrick Agyemang and in his first raid was brought down in the penalty area by Zigor Aranalde but the Dons were denied a spot kick.
Without any shadow of doubt the game was dominated by the poor pitch conditions. Neither side could master the heavy going and this was reflected in the poor standard of play.
Walsall's attacking problems were highlighted by the fact their strikers could pose few problems for Wimbledon's defence despite the Saddlers being given plenty of space down the flanks.
The best chance to fall to Walsall occurred in the 59th minute when the ball bobbled into the path of Aranalde but the Spanish defender aimlessly shot wide.
In this spell the Saddlers were well top but there was a general reluctance to shoot even when they had progressed deep into Wimbledon's penalty area.
Darren Wrack eventually broke clear following an astute pass from Danny Sonner but goalkeeper Kelvin Davis, who had a fine game, advanced from his goal to smoother the low shot.
The stalemate was broken in the 75th minute when Jorge Leitao pulled a ball back into the path of Zdrilic to hammer his right-footed shot low past Davis to the relief of the home crowd.