The Northern Irishman rose from eighth to second behind Australian Adam Scott, who retained top place after finishing tied for fifth at the Royal Liverpool course.
It was McIlroy's third major title and he is now three-quarters of the way to a grand slam of majors at the age of 25.
Henrik Stenson of Sweden, who finished down the field after shooting 287, fell one place to third and Englishman Justin Rose slipped from third to fourth.
Spaniard Sergio Garcia climbed from ninth to fifth after finishing as runner-up to McIlroy, the fourth time in his career he has been second at a major championship.
Bubba Watson, who missed the Open cut, dropped two places to sixth while fellow-American Matt Kuchar fell from fifth to seventh.
Australian Jason Day was another to slip two places, from sixth to eighth, while Tiger Woods and fellow-American Jim Furyk, who finished fourth in Hoylake, complete the top 10.
(Reporting by Ed Osmond, editing by Ed Osmond)
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