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.
"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)
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