The match was delayed by over an hour due to heavy thunderstorms in New York and both players struggled to adapt to the windy conditions when they emerged on Arthur Ashe Stadium.
After exchanging early breaks it was Berdych who coped with the strong winds better, and the Czech broke again before taking the opening set 7-5.
However, Murray broke instantly in the second and began to use the blustery conditions to his advantage with a variety of shots around the court.
A second break then saw him establish a 4-1 lead and he went on to clinch the second set with little trouble 6-2.
The third was even simpler for the Scot as Berdych made a number of unforced errors in the wind to help him win 6-1.
Murray converted his fifth break point at the start of the fourth set to seize control of the contest, but Berdych quickly broke back during a brief resurgence.
Both players continued to hold serve to force the tie-break before Murray closed out the match 9-7.