South Korean Yang, who outdueled Tiger Woods to win the 2009 U.S. PGA Championship, shot a one-under-par 71 in the final round of the six-round event to finish with an eight-under total of 420.
Molinari, who made his solitary Ryder Cup appearance along with brother Francesco at the 2010 edition in Wales, shared second place on 416 after a closing 74.
The tournament was won by little-known Englishman Nathan Kimsey, who carded a final-round 70 for a 415 tally.
"I literally have no words," said Kimsey. "Going out there today I was just trying to keep the nerves down and keep calm, keep making good swings, find greens and make it easy for myself.
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"I couldn't even have thought about winning. Becoming a European Tour player means everything right now."
(Writing by Tony Jimenez in London; Editing by Larry Fine)
