A week on from their 4-1 derby humiliation at City, United were looking to return to winning ways in the league but instead slumped to a 2-1 defeat yesterday that left the champions in 12th place in the table.
On-loan Marseille winger Morgan Amalfitano put West Brom ahead with an exquisite individual goal in the 54th minute, picking the ball up on halfway and nutmegging Rio Ferdinand before insouciantly dinking the ball over goalkeeper David de Gea.
Steve Clarke's side held on for a victory that means United have now made their worst start to a season since 1989, in Moyes's first campaign since succeeding the legendary Alex Ferguson as manager.
"It was a poor result and a poor performance," said Moyes. "We never really got going. We had a lot of the ball in the first half and never made many chances from it. They always looked a threat on the break, in the first half especially, and even more so in the second half. We missed that spark and West Brom deserved it, no question. I can't argue with that."
Yaya Toure gave City the lead on the stroke of half-time, with Edin Dzeko putting the visitors back in front in the 56th minute after Karim El Ahmadi had equalised for Villa early in the second period.
However, a fine free-kick from Leandro Bacuna saw Villa equalise in the 73rd minute before Andreas Weimann ran clear and beat Joe Hart two minutes later to give Paul Lambert's side a stunning win.