Albion remain six points clear of the drop zone tonight.
And they could face a demoralised Blackpool when they return to Championship action next Saturday.
Wigan remain second from bottom after they lost 1-0 at home to Huddersfield, who ease their own relegation concerns.
Conor Coady fired the 82nd-minute clincher from a tight angle.
Chris Hughton's men also have a handy goal-difference advantage over 22nd-placed Millwall.
Bottom side Blackpool were humiliated 7-2 at Watford having led 2-0 at the interval.
Odion Ighalo led the second-half goal rush for the Hornets with four.
It had all looked so promising for Blackpool when ex-Albion midfielder Andrea Orlandi smashed home on just eight minutes after indecisive defending.
It was his first goal for Blackpool.
Charlton picked up a 0-0 draw at Wolves in Guy Luzon's first game in charge.
The Addicks are now three points clear of Albion.
Brentford won 2-1 at Norwich in the pick of the day's four Championship fixtures, Alex Pritchard converting a decisive 71st-minute penalty.
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