Two goals in as many second half minutes gave the home side the momentum to go on and score four goals for the first time this season.
Millwall were hoping to build on their positive display against Norwich in midweek, but injuries forced Rowett to leave Jed Wallace, Danny McNamara and Ben Thompson on the bench.
The changes seemed to disrupt the Lions, who struggled to string passes together, creating their own problems in defence throughout the first half.
The Owls took advantage of the hosts' disjointed start, when Elias Kachunga capitalised to drive into the box. Calum Paterson finished second time of asking, giving his side the lead on 10 minutes.
There was little sign of fight back from Millwall, who struggled to cause Chey Dunkley and Tom Lees problems with long balls.
Ryan Leonard, back in midfield after filling in in the back three, was the Lions main threat. He couldn’t make the most of a two on one on the break, putting his square pass behind Ken Zohore who would have had a free shot at goal.
Millwall’s lifeline came through Leonard on 39 minutes when Joey Pelupessy needlessly pulled him to the floor in the box. Zohore stepped up to rifle home the penalty.
Rowett brought Thompson on at half time, a positive change to give Millwall some more thrust in the midfield. The hosts started the half on top and were unlucky not to take the lead on 54 minutes.
Bodvarsson, who had had a quiet first half, cut inside on his left foot and saw his deflected effort well saved by Keiren Westwood.
The Owls’ keeper was on hand to deny the Lions from the resulting corner. Shaun Hutchinson’s powerful header was turned around the post by the former Irish number one.
Momentum stayed with the Lions, who continued to press for the lead. A quick free kick from debutant George Evans set Ben Thompson in behind, but his low, driven effort was well saved by Westwood.
The home side got the breakthrough they deserved on 68 minutes, a wonderful solo goal by Scott Malone, who chipped the ball over a Wednesday defender before volleying home.
And the action didn’t stop there, as Thompson doubled the lead a minute later. Was it a cross or was it a brilliant effort from the right side of the area? Either way, it dipped over Westwood and nestled into the side netting.
The icing on the cake came as the home side added a fourth. Mahlon Romeo drove from within his own half to the edge of Wednesday box before his effort flicked off of Tom Bradshaw and into the bottom corner.
It was a well deserved victory for Millwall in the end, who recovered from a poor start and went on to dominate the second half. Rowett will be happy with the two individual bits of quality that gave the Lions the win, his side did plenty to earn the three points in the second half.
Teams:
Millwall: Bialkowski; Romeo, Evans, Hutchinson, Cooper, Malone; Leonard (Williams, 60), Woods, Kieftenbeld (Thompson, 46); Bodvarsson (Smith, 85), Zohore (Bradshaw, 79)
Subs: Fielding, Pearce, Bennett, McNamara
Sheffield Wednesday: Westwood; Palmer (Shaw, 59), Lees, Dunkley, Hutchinson (Urhoghide, 73); Reach, Bannan, Pelupessy, Penney (Harris, 46); Kachunga (Rhodes, 59), Patterson (Windass, 73)
Subs: Wildsmith, Borner, Green, Brown
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