The top seeds beat Croatia’s Ivan Dodig and Marcelo Melo of Brazil 3-6, 6-3, 6-4, 6-4.
The brothers, taking part in their 25th Grand Slam final, had also won the Olympics in 2012.
They now have 15 men’s doubles titles at the Grand Slams, and extended their winning streak to 24 matches.
Ken McGregor and Frank Sedgman are the only pair to have completed the calendar Grand Slam back in the pre-Open era of 1951.
Bouncing back
The top-seeded twins lost the first five games of the match but fought back strongly to outclass Dodig and Melo, and extend their Grand Slam record number of titles to 15.
The 35-year-old Bryans, who also won the Olympic gold medal last year, got the measure of their 12th-seeded opponents through the telepathic understanding which has brought them 91 career doubles titles.
They made the decisive break in the ninth game of the fourth set, and Bob Bryan served it out for victory which he sealed with an ace, prompting a trademark chest-pump by the brothers.
If they win the U.S. Open, they’ll join McGregor and Sedgman as the second men’s team to complete a calendar Grand Slam. The Aussie duo did it in 1951, 17 years before the Open era began.