While the American was sliding down the leaderboard, Dane Soren Kjeldsen was taking a grip of the European Tour event, a four-under 67 giving him a two-stroke advantage over the field on seven-under 206.
Fowler holed a chip shot for an eagle two on 16 to move to two-under-par but then sent his tee shot out of bounds before losing his third in gorse bushes as he slumped to a quadruple bogey.
He found more trouble at the last, again driving out of bounds en route to a triple bogey as he plunged to a 76 for 218.
Fowler, who won the Players Championship in Florida earlier this month, declined to comment after his round.
Kjeldsen also came unstuck over the closing two holes, ending with two bogeys to see a four-shot lead cut to two strokes.
"It surprised me somewhat that it seemed such easy going for the first 13 holes on what was another tough day,” he told reporters. "But the course got some back from me on 17 and 18.
"Eventually this course is going to get you so overall it was still an excellent day's golf.
"I didn’t hit a great tee shot on 17 and then hit two good putts on 17 and 18 but they didn’t drop."
German Maximilian Kieffer returned a 65 for 208 to share second place with Spain's Rafa Cabrera-Bello (69).
British pair Richie Ramsay and Tyrrell Hatton were tied for fourth position with Bernd Wiesberger of Austria on 209.
(Editing by Tony Jimenez)
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