Arsene Wenger's men have won only three matches since January 31st; two of which were in the FA Cup against clubs from England's fifth division.
Craig Dawson scored twice from corner kicks - firstly to put West Brom 1-0 ahead, secondly to seal victory.
Arsenal initially fought back after Dawson's first goal through an Alexis Sanchez equaliser - the eighteenth time this season that Chilean has scored - but were trailing once more after half time, when Hal Robson-Kanu found the net with only his second touch of the game, after coming on as a substitute.
The clash in Birmingham was also notable because of two aeroplanes flying over The Hawthorns with large banners attached. The one in support of Wenger continuing as manager read: "In Arsene we trust, respect AW." The anti-Wenger banner: "No contract, Wenger out."
Those supporters that want a change at the Emirates Stadium after twenty seasons were loudest towards the end of the match, booing the decision to bring off Sanchez in the 78th minute.
Arsenal have now lost four of their last five Premier League games for the first time since April 1995.