Alex Neil’s side dropped beneath Newcastle and Sunderland prior to kick-off, when a side showing five changes aimed to respond to the 3-0 loss to the Black Cats.
Norwich started well. Nathan Redmond forced Petr Cech to save after five minutes, after a Martin Olsson cross evaded everyone.
Cameron Jerome blasted over before arguments broke out between Arsenal supporters disputing the future of their club.
“There’s only one Arsene Wenger” rang around the Emirates Stadium as the 12th-minute protest took place.
There was indecision off the field and on it, as Arsenal dithered around the Norwich penalty area, failing to fashion any real chances.
A deflected Mohamed Elneny effort resulted in a corner and Laurent Koscielny headed over.
Gary O’Neil had an opportunity on the break, exchanged passes with Redmond, but miscued his shot spectacularly over.
Redmond, Norwich’s most lively player, made space for a shot which skipped wide.
Then came Welbeck’s introduction, immediately injecting energy, and Arsenal’s goal.
Redmond tried to create an equaliser, crossing for substitute Dieumerci Mbokani, but Gabriel – on for the injured Per Mertesacker – timed his intervention brilliantly.
Alexis Sanchez shot straight at John Ruddy from a Mesut Ozil pass on the counter attack.
The Germany playmaker then volleyed over before Elneny brought the ball down on his chest and fired with the outside of his boot. Ruddy saved.
The goalkeeper ventured forward in stoppage time, but Norwich’s free-kick barely reached him as they suffered another damaging defeat.