The unseeded Indo-Pak combination suffered a 5-7 1-6 defeat against their top seeded rivals in the euro 3,452,415 clay court tournament, the second last event in the run up to the French Open.
Bopanna and Qureshi could break the American twins only one time while they dropped serve four times in the match, which lasted just 65 minutes.
They split euro 11080 as prize money and earned 90 ATP ranking points each for the effort.
The fifth seeded Indo-Zimbabwean pair recorded a 6-3 6-4 win over Daniela Hantuchova and Mirjana Lucic-Baroni in one hour and 70 minutes in the second round of the euro 2,120,000 premier WTA event.