The Championship side had taken the lead in the first-half after a thumping Reda Johnson header but the Silkmen have proved themselves already in the cup this season.
A 4-0 thumping of League 1 Swindon in round one served noticed of their credentials and Williams poked home the equaliser as the hosts threw men forwards after the break.
Wednesday pushed for a winner but it was not to be and a replay will be a huge financial boost to cash-strapped Macclesfield who have struggled since relegation from the Football League in 2012.
It was hard to tell which side was three divisions above the other in the opening exchanges with Jack Mackreth looking dangerous down the Macclesfield right.
By contrast Wednesday were struggling to find any rhythm, typified when Johnson’s left-wing cross went straight out of the ground.
The hosts almost got the lead their play deserved when Mackreth’s corner was guided towards the far corner by Joe Connor but Liam Palmer hacked it off the line.
The Owls grew into the game, however, and began to look dangerous on the counter attack and they were rewarded just after the midway point of the first half.
Jeremy Helan won a corner despite the home fans’ protestations, and from Stephen McPhail’s resulting delivery Johnson powered home his second of the season.
The lead should have been doubled soon after but Rhys Taylor produced a superb save to deny Atdhe Nuhiu from close range.
And they were almost punished when a loose touch from Damian Martinez presented Scott Boden with a chance but the Owls keeper did just enough to force him into touch.
After the break McPhail dragged a long-range effort well wide for Wednesday but the non-league side then began an assault on the visitors’ goal.
The Silkmen looked particularly threatening from corners with Palmer repeating his goal-line heroics, this time to deny Chris Holroyd before Boden hit the side-netting from another delivery.
Wednesday’s only chance of the half fell to Helan who was denied by another fine save from Taylor.
Danny Whitaker then went on a mazy run before his tame effort was held by Martinez and the keeper then produced a stunning save to deny the same man’s shot from inside the box.
The goal was coming for Macclesfield, though, and after throwing men forward it was centre-back Williams who found space from a right-wing cross to poke low into the far corner across the keeper.
Wednesday, with only one away win to their name all season in all competitions, pushed hard late on but never really looked like finding the winner and the Silkmen make the fourth round draw for the third successive year.