Bjorn shot a 6-under 65 in the final round to forge a 72-hole deadlock with Lee at 20-under 264.
Lee, who shot a course-record 61 Saturday, settled for a 4-under 67 Sunday.
His drive on the ensuing playoff hole landed in a fairway bunker but he put his second shot within 20 feet of the pin and two-putted for par.
Bjorn drained a birdie putt to clinch his 14th European Tour victory and first since the 2011 European Masters.
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