Leon Osman spared Everton's blushes with a late equaliser as Championship rivals Millwall came close to a shock.
Striker Marvin Williams, 18, gave the home side a first-half lead on his full debut, racing clear before beating Richard Wright in the Everton goal.
But the visitors hit back strongly, putting Millwall's goal under siege as they went in search of an equaliser.
Sub Osman finally broke Millwall's resistance after 79 minutes, his close-range header earning a replay.
Everton had left top scorer James Beattie and veteran Duncan Ferguson on the bench after the holiday programme - and it was Millwall old boy Tim Cahill who had the majority of first-half chances.
He volleyed over in the opening seconds before Millwall keeper Andy Marshall was forced to save Marcus Bent's header with his legs.
Millwall almost took the lead after 27 minutes, but Tony Hibbert was perfectly placed to kick Ben May's header off the line.
Everton then wasted a glorious double chance to break the deadlock five minutes later.
James McFadden shot straight at Marshall when he looked certain to score, and Cahill fired the rebound wildly over the top.
Millwall finally opened the scoring on 38 minutes, Williams outpacing Matteo Ferrari to score past the advancing Wright.
Cahill had two further opportunities in first-half injury time, Marshall tipping one header over the bar and Kevin Braniff clearing another off the line.
Millwall had a glorious chance to extend their lead two minutes after the interval but Marvin Elliott headed over from point-blank range.
Everton made a double substitution on the hour, sending on Beattie and Ferguson for Bent and McFadden.
After Ferguson's far-post header had been blocked, the visitors finally levelled with 11 minutes to go, Kevin Kilbane finding Osman, who headed in after his first shot had been blocked by Marshall.
Osman then brought an acrobatic save out of Marshall and Kilbane fired over as Everton came close to a dramatic winner.
Millwall: Marshall, Robinson, Lawrence, Whitbread, Craig, Williams, Elliott, Livermore, Cogan, May, Braniff (Fangueiro 83).
Subs Not Used: Phillips, Weston, Pooley, Hendry.
Goals: Williams 39.
Everton: Wright, Hibbert, Weir, Ferrari, Nuno Valente, Arteta, Cahill, Neville (Osman 74), Kilbane, Bent (Ferguson 59), McFadden (Beattie 59).
Subs Not Used: Turner, Naysmith.
Booked: Arteta, Weir.
Goals: Osman 79.
Ref: R Styles (Hampshire).