The pair dropped their rackets and embraced in the middle of the court after Ebden's return landed in the net on match point to complete the comeback and extend their winning streak at Flushing Meadows to 18 matches.
Bopanna and Ebden dominated the first set, breaking serve in the opening game of the match and capturing it with a love hold.
They appeared to be carrying the momentum into the second set when Bopanna raced across the court and ripped a one-handed backhand winner down the line in the third game.
But Ram raised his level from there and the duo finally broke serve when Bopanna's forehand sailed long for a 4-2 second set lead before they levelled the contest at a set a piece with an ace from Ram out wide.
Bopanna's aggressive forehand landed wide to hand Ram and Salisbury a break and a 3-2 lead in the decider that they would not relinquish on a hot and humid day at Arthur Ashe Stadium.
The American Ram and Briton Salisbury are the first men's doubles team to win three straight US Open men's doubles titles in the Open era. The last team to accomplish the feat was Tom Bundy and Maurice McLoughlin from 1912-1914.
