A tap-in by Cesar Azpilicueta and an own goal by Gareth McAuley were cancelled out either side of halftime by fine strikes from outside the box by Craig Gardner and James McClean.
Struggling Chelsea, who were hovering just above the relegation zone until recently, are now unbeaten in five league games, a run which began immediately after the departure of Jose Mourinho, the most successful manager in the club's history.
But they remain in the bottom half of the table and their only chance of silverware this season lies elsewhere.
Hiddink said the prospect of claiming one of the four Champions League spots was looking harder.
"As long as it is possible to get, mathematically, the fourth position in the Champions League, then we go for it," he told reporters.
"But then we have to win all the games at home at least."
Hiddink said in his programme notes that the club was taking the FA Cup "very seriously".
The London club will also fight for a place in the Champions League last eight against Paris Saint Germain when the competition resumes next month.
West Brom coach Tony Pulis praised his players for getting back into the match.
"The lads worked hard enough as a team and as a group to get something out of the game," he said.
(Editing by Ed Osmond)
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