An eighth loss left the Owls with their worst ever start to a season from the first 10 games, and they are already seven points adrift of the safety line.
John Swift’s 13th-minute goal settled the match with the Owls having now gone 312 minutes without a goal, with their only points so far coming from draws against Middlesbrough and at Leeds.
But it could have been different if Juan Delgado and Tyreeq Bakinson had converted early chances for the visitors.
Munoz rang the changes – seven – from Friday night’s 3-0 home defeat to Sunderland.
It mattered little as West Brom dominated the game of few opportunities as their fifth game unbeaten saw them climb to fifth.
Carlos Corberan’s side started by forcing numerous corners and crosses from which the recalled Brandon Thomas-Asante and Kyle Bartley missed the target.
West Brom took the lead with a goal of classic simplicity. Darnell Furlong played the ball down the right, Akin Famewo missed the chance to cut it out and Jed Wallace crossed low for Swift to sweep it high into the net from six yards.
Swift’s fifth goal of the season soon had the near 2,000 Wednesday fans calling for Munoz’s head but just after the goal, the Owls created two excellent chances.
The sliding Delgado missed Ashley Fletcher’s cross, then Bakinson’s curling shot was clawed away by goalkeeper Alex Palmer.
The Baggies dominated in the second half but were their own worst enemies as they overplayed in front of goal rather than opting to shoot.
West Brom: Palmer, Kipre, Bartley, Pieters, Furlong, Yokuslu, Mowatt, Phillips (Townsend 69), Thomas-Asante (Diangana 86), Swift (Chalobah 90), Wallace. Unused substitutes: Ajayi, Molumby, Pipa, Fellows, Griffiths, Taylor.
Sheffield Wednesday: Vasquez, Palmer, Iorfa, Bernard, Famewo, Delgado (Valentin 58), Bakinson (Hendrick 76), Vaulks (Buckley 77), Musaba (Wilks 76), Smith, Fletcher (Gassama 64). Unused substitutes: Dawson, Byers, Gregory, Paterson.
Referee: J Busby (Oxfordshire).