Joey Pelupessy opened the scoring with his first goal for the Owls three minutes before the break.
But second-half efforts from Lee Gregory and Steve Morison handed Millwall all three points.
While the hosts dominated possession throughout the first half, they created little beyond a chance for Gregory which the forward struck narrowly wide and Ben Marshall’s curling effort which was deflected onto the left post.
They appeared under little pressure but in the 42nd minute, Dutch midfielder Pelupessy, a January signing, punished them with a fine goal against the run of play.
After collecting Jack Hunt’s clearance, without warning he cut inside onto his right foot and from the edge of the area powerfully bent inside the far, top right corner.
Having rarely looked like scoring, Millwall netted their equaliser only seven minutes into the second half, through Gregory.
From a free-kick on the right, Shaun Williams crossed towards Jake Cooper, who headed back across goal to gift Gregory the close-range header he powerfully sent high into the back of the net.
With the momentum theirs, Millwall scored again 11 minutes later.
When Wednesday defender Jordan Thorniley went down clutching his face when vying with Jed Wallace for a loose ball, the winger squared to Morison, who from in front of goal and unchallenged, scored with a low, routine finish.
After a delay, Thorniley was taken off on a stretcher, and Wednesday, who remain 16th, offered little response, even with 13 minutes of added time.