The fifth-seeded Bopanna and Babos lost 6-2 4-6 9-11 to the Croat-Canadian pair of Pavic and Dabrowski, seeded eighth.
Rohan Bopanna and his partner Pablo Cuevas had lost their US Open men's doubles second round match to Fabio Fognini and Simone Bolelli.
The Indo-Canadian duo of Rohan Bopanna and Gabriela Dabrowski lost a two-hour quarter-final battle in the mixed doubles event.
The Indo-Canadian pair of Rohan Bopanna and Gabriela Dabrowski beat the Columbian-German pair of Robert Farah and Anna-Lena Gronefeld 2-6, 6-2, 12-10 to win the mixed doubles French Open title.
India's Rohan Bopanna earned himself an opportunity to become only the fourth Indian to win a Grand Slam trophy by reaching the French Open mixed doubles final with partner Gabriela Dabrowski
Rohan Bopanna and his Canadian partner Gabriela Dabrowski stormed into the semifinals of the mixed doubles event of the French Open with a straight-set upset win over the duo of Sania Mirza and Ivan Dodig of Croatia on Monday
The Indo-Canadian combo notched up a facile 6-0, 6-1 win over Australian pair of Jessica Moore and Matt Reid.
Sania Mirza and Ivan Dodig just managed to edge past Rohan Bopanna and Gabriela Dabrowski to enter the Australian Open mixed doubles semis.
The Indo-Canadian pair of Rohan Bopanna and Gabriela Dabrowski suffered an agonising defeat in their US Open mixed doubles quarterfinal match against Anna Lena-Groenefeld and Robert Farah
While Sania Mirza and Rohan Bopanna advanced in the 2016 US Open, Leander Paes failed to progress past the second round in the mixed doubles event