Goals from Murray Wallace, George Saville, Wes Harding and Brooke Norton-Cuffy gave the Lions a convincing victory in Edwards' first game at the club, while Wednesday's miserable Championship campaign continues.
Wednesday manager Danny Rohl made two changes to the team that lost 1-0 at Bristol City last weekend, with Marvin Johnson and Ashley Fletcher coming in.
Edwards made just one switch from the side that lost at home to Southampton, with Ryan Longman joining the starting XI.
Wednesday's best chance of the first half came when skipper Barry Bannan played in Anthony Musaba but he lost his composure and blazed well over the bar.
Millwall took the lead after 31 minutes. George Honeyman whipped in a corner from the left and Wednesday were nowhere to be seen, leaving Wallace completely unmarked for the defender to place a bullet header into the net.
Saville then doubled the advantage three minutes before the interval with a terrific effort from range. Cameron Dawson was at full stretch but the ball curled beautifully away from the Wednesday keeper.
Wednesday made a trio of changes after the break, with Jeff Hendrick and Josh Windass brought on and Bailey Cadamarteri making his first league appearance for the club to try and get the Owls back in the game, but the away side's dominance continued.
Millwall added their third in the 52nd minute when Dawson spilled a cross and Harding was there to tap in from close range.
Owls fans were further frustrated when Windass had a penalty claim dismissed for an apparent handball in the Millwall penalty area.
Cadamarteri and Callum Paterson both had chances to get one back for Wednesday but Bartosz Bialkowski was there to save on both occasions.
Norton-Cuffy added further shine to the scoreline in the 72nd minute, driving in from the right and finishing calmly into the bottom corner. The home fans headed for the exits while the Millwall supporters were bouncing.
Victory sees Millwall move up the table to 15th but Wednesday remain rooted to the bottom of the table, Rohl with four losses out of his first five games at the club.