Owls boss Paul Sturrock had warned of complacency after their 1-0 win but Wednesday failed to put away their chances as Millwall struck twice after the interval.
Wednesday started brightly, Manchester United teenager Chris Eagles, on loan at Hillsborough until Christmas, almost snatched a dramatic opener on nine minutes after striker Lee Peacock was hauled down.
The 19-year-old England youth international produced a carbon copy strike of the goal that felled Leeds in midweek but this time his curling 25-yard free-kick dropped the wrong side of the bar.
The impressive Eagles carved out an opening for David Graham on 17 minutes threading the ball into his path but the Wednesday striker, signed from Wigan in the summer, hesitated and Marcus Phillips cleared.
Wednesday, chasing their second successive win, almost snatched the opener in the 25th minute after Jamie Vincent blundered. The Millwall full-back pulled the ball back to Andy Marshall and Peacock nipped in to connect only for his shot to be blocked by the Millwall keeper.
Graham should have broken the deadlock seconds before half-time, Peacock setting up his co-striker with a precise cross from the left flank but from six yards he pulled his header wide.
Wednesday were punished for squandering those chances in the 49th minute. Alan Dunne drilled in a close-range shot that was stopped on the line by John Hills and Barry Hayles slammed the loose ball past the helpless David Lucas.
Marshall then kept out Peacock when he smothered his low drive after Glenn Whelan's cross had been headed down by substitute Lee Bullen.
Wednesday were back on level terms in the 65th minute. Millwall failed to clear Chris Brunt's corner and centre-back Graham Coughlan finished clinically with a header at the far post.
Millwall hit back nine minutes later, Jermaine Wright crossing to the waiting Carl Asaba, on for the injured Ben May, who beat Lucas with a text book header from six yards.