The unseeded Indian combine lost 3-6 2-6 to the second seeded Croat-Brazilian combo in the quarterfinal, which was over in just 51 minutes.
Paes and Bopanna play with different partners on the ATP tour and hence playing against a formidable team, which has done extremely well this season, was a tall order.
Melo and Dodig reached the US Open semi-finals and also reached finals of two Master series events — Canada and Monte Carlo — this year.
The Indian pair had just one chance to break their opponents and lost their serve thrice in the contest.
Paes and Bopanna had beaten local wild card pair of Tatsuma Ito and Go Soeda in their opening round.