Having been outplayed in the first half Leon Osman met a clearance from James Jennings with a powerful half-volley that was still on the rise as it hit the top corner from 22 yards.
Macclesfield should have taken the lead on ten minutes when Jennings floated an inch-perfect cross to the far post, where Nat Brown planted a free header horribly over the crossbar from just six yards.
Youngster Izak Reid had another chance for the home team in the 16th minute, but could only blaze a 15-yard drive over the bar.
Tim Cahill should have put Everton in front in the 31st minute when a long throw from Phil Neville deflected into his path, but he could only scuff a left-foot shot straight at Macclesfield keeper Jon Brain.
Everton dominated the second half. Striker Victor Anichebe nearly extended their lead on the hour with a viciously curling shot from 25 yards that grazed the crossbar.
They again went close moments later when centre-back Phil Jagielka produced a superb scissors kick which lobbed on to the roof of the net.
Jagielka again ventured forward in the 74th minute, but could only poke a volley just over the crossbar from 15 yards.
Macclesfield had appeals for a penalty in the 84th minute waved away when Tony Hibbert looked to have brought down Danny Thomas on the edge of the box.
Thomas then went close in the 89th minute with a drive from the edge of the box which flew inches over the bar.
With the last kick of the game Macclesfield nearly forced a replay when veteran striker Simon Yeo forced a stunning save from Tim Howard with a powerful 20-yard volley.