The second-seeded Indian pair bounced back to win the title clash 2-6, 6-3, 10-4 against Chinese Taipei's combo of Tsung-hao Huang and En-shuo Liang.
Ankita, Rutuja progress to pre-quarterfinals
The 43-year-old Bopanna, coming out to play his 33rd and final tie, and Bhambri raced to a 6-2, 6-1 win over Elliot Benchetrit and Younes Lalami Laaroussi.
Rohan Bopanna at 43 was hoping to become the oldest winner of a Grand Slam.
Bopanna beat the record of Daniel Nestor of Canada, who was 43 years and four months when he played in a Major final, by two months.
The sixth-seeded Indo-Australian pair defeated the American duo of Nathaniel Lammons and Jackson Withrow in the quarterfinals.
Bopanna and Ebden, who are seeded sixth, brushed aside the Australian duo in less than an hour.
Digvijay Pratap Singh is the new face in the six-member team.
They lost in straight sets to top seeds Wesley Koolhof of the Netherlands and Great Britain's Neal Skupsk in the semifinals.
Overall, Bopanna, a US Open runner-up in 2010, has made four Grand Slam semifinals in the men's doubles