The American needed to chip in from the bunker on the final hole to force a playoff but his shot went wide, leaving Fleetwood, watching on TV in the clubhouse, to celebrate his third European Tour victory by hugging his family.
The 26-year-old from Southport, who went into the final round one shot behind co-leader Uihlein, finished on 12-under par.
Swede Alexander Bjork, Frenchman Michael Lorenzo-Vera and Thorbjorn Olesen of Denmark finished four shots off the pace.
"I didn't mis-strike a shot at all," said Fleetwood, who last month finished fourth at the U.S. Open.
"I played great today. I felt comfy. It's always great to test your game and test what you work on every day under the ultimate pressure."
(Reporting by Neil Robinson in London; Editing by Ken Ferris)
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