Im had a 68, four under par, and Rahm a 67.
Japan's Hideto Tanihara was fourth, 15 under and Frenchman Julien Quesne made big strides by shooting 64 to lie one shot behind him.
In all nine players, including Britain's Justin Rose, were within four strokes of the lead.
Tournament host Rory McIlroy was not involved after missing the cut on Friday.
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(Reporting by Steve Tongue; Editing by Stephen Powell)
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