Albion can move up a place in time for Christmas – but they need to win at home.
Victory at home to Sheffield United would see the Seagulls into 15th spot and above Arsenal, who lost 2-1 at Everton.
That would be an improvement on the 16th place in which they began this round of games.
It also appears the Gunners could be without Pierre-Emerick Aubameyang for the Christmas programme, which includes a trip to the Amex.
The striker missed the Goodison Park contest with a calf problem.
Arsenal boss Mikel Arteta said: "We want him as quickly as possible. He has a small strain and will need a few days.
THE FACTS BEHIND THAT RECORD ALBION DON'T WANT TO BREAK
"I don't know if it is a week or two weeks, it depends how the injury goes."
Nicolas Pepe's first-half penalty equaliser of Rob Holding's own goal counted for nothing after Yerry Mina headed the winner on the stroke of half-time.
Fulham missed the chance to go above Albion as they let slip a lead in a 1-1 draw at Newcastle.
Matt Ritchie's unfortunate own goal was cancelled out by a Callum Wilson penalty after a foul by Joachim Andersen, who was sent off.
Fulham move on to ten points, which is one fewer than Albion and the same as Burnley, who host Wolves on Monday.
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