With Bopanna's defeat, India's challenge has ended in the elite clay-court tournament.
Six-time champion Novak Djokovic has withdrawn from this year's Italian Open, organisers said on Tuesday.
Jannik Sinner equalled Novak Djokovic's all-time record of 31 Masters 1000 wins in a row after defeating Andrea Pellegrino at the Italian Open.
Jannik Sinner surpasses Novak Djokovic's record with his 32nd consecutive Masters 1000 victory, advancing to the Italian Open semi-finals after defeating Andrey Rublev.
World number three Novak Djokovic came back from a set down to beat unseeded Swiss Stanislas Wawrinka 4-6, 6-3, 6-3 and claim the Rome Masters title on Sunday.
Federer's bid to win his first title on the clay courts of the Rome Masters juddered to a premature halt on Wednesday when he lost his second-round clash against Spain's Albert Costa 3-6, 6-3, 6-2.
Ailing Briton Andy Murray suffered another setback to his French Open preparations as he was ousted 6-7, 6-3, 6-2 by Richard Gasquet in the third round of the Rome Masters on Thursday.
With Carlos Alcaraz out, the French Open men's singles draw is wide open. Clay-court specialists and rising stars are vying for the title at Roland Garros.
The seventh seed Indian pair of Mahesh Bhupathi and Rohan Bopanna crashed out of the ATP Rome Masters after suffering a straight-sets defeat at the hands of Marcel Granollers and Marc Lopez, in Rome.
Roger Federer settled a score with his bogey player Guillermo Canas on Tuesday, easing his way into the third round of the Rome Masters with a 6-3, 6-3 victory.
Russian Maria Sharapova ground down Carla Suarez Navarro 4-6, 7-5, 6-1 to win the Rome Masters final on Sunday, the 35th WTA Tour title of her career.
Four-times Grand Slam champion Alcaraz, who is gearing up to defend the French Open title later this month, fired off 24 winners in a strong performance to seal victory.
Meanwhile, in the WTA event, third seeded-pair of Sania Mirza and Yaroslava Shvedova lost 3-6, 6-7(7) to second seeds Yung-Jan Chan and Martina Hingis in the semi-finals of the $3,076,495 red clay event.
Third seed Andy Roddick lost 6-0, 6-4 to last 16 opponent Juan Ignacio Chela.
Rohan Bopanna and Pablo Cuevas came from behind to knock out seventh seeds Feliciano Lopez and Marc Lopez, sealing a quarter-finals berth at the ATP Rome Masters.
They are yet to play a match in the men's doubles event at the Rome Masters.
The world number one went down to Spain's Albert Costa in the second round of the Rome Masters.
Second seed Andy Roddick crashed out in the first round of the Rome Masters, losing 7-6, 6-1 to Guillermo Canas.
The Briton he lost in the third round to slow court specialist Mariano Zabaleta.
Backed into a corner, world number five Paolini mounted a comeback of her own in the second set, winning six successive games after herself trailing 4-0.
Third seeds Leander Paes and Mahesh Bhupathi crashed out of the Rome Masters after being outplayed in the super tie-breaker by Americas Sam Querrey and John Isner in the second round. The ace Indian pair was beaten 3-6, 6-3, 5-10 by their unseeded opponents in 72 minutes.
Rafael Nadal enjoyed the perfect fillip ahead of his French Open defence with a commanding 7-5, 6-3 victory over world number one Novak Djokovic in the delayed Rome Masters final on Monday.
Jannik Sinner was two games away from the Italian Open final when heavy rain suspended his semi-final match against Daniil Medvedev, with Sinner leading 6-2, 5-7, 4-2.
Ben Shelton said he had laid down a claycourt marker for US men with his Munich Open win on Sunday after the World No. 6 became the first American to claim an event above the ATP 250 level since Andre Agassi's 2002 Rome Masters triumph.
Mahesh Bhupathi and Rohan Bopanna ended runners-up at the Rome Masters after a tame straight sets defeat at the hands of top seeded American team of Mike and Bob Bryan in Rome on Sunday.
Holder Novak Djokovic took advantage of Roger Federer's slump after a rain break to win 4-6, 6-3, 6-3 on Saturday to set up a Rome Masters final against world number one Rafael Nadal. Nadal, a triple champion here, powered past Chilean 12th seed Fernando Gonzalez 6-3, 6-3.
The third seeded Indo-Czech pair beat Romanian Andrei Pavel and Germany's Alexander Waske in the quarter-finals.
Third seeds Leander Paes and Lukas Dlouhy moved to the quarter-finals of the ATP Rome Masters after getting a walk-over from Croat Ivan Ljubicic and Michael Llodra of France in the second round.
Mahesh Bhupathi and Rohan Bopanna entered the quarter-finals of the Rome Masters, but it was curtains for Leander Paes and his Austrian partner Jurgen Melzer.
Czech Tomas Berdych snapped a run of 11 consecutive defeats by world number one Novak Djokovic to reach the semi-finals of the Rome Masters before Rafael Nadal was stretched to the limit against David Ferrer on Friday.
World No. 1 Novak Djokovic beat Roger Federer in straight sets on Saturday and will play Rafa Nadal in the Rome Masters final for the second year in a row.
Carlos Alcaraz will not defend his French Open title next month after tests on his injured wrist revealed he would not be ready in time, the world number two said on Friday.
Sania Mirza and Martina Hingis of Switzerland stormed into the semi-finals of the Rome Masters with a straight-set victory over Julia Goerges and Silvia Soler-Espinosa on Thursday.
Rohan Bopanna and Aisam-ul Haq Qureshi failed to get past the formidable United States' combination of Mike and Bob Bryan, losing in straight sets in the second round of the ATP Rome Masters, on Thursday.
Prime Minister Narendra Modi presented a range of culturally significant gifts during his recent five-nation tour, including a Muga silk stole for the Italian Prime Minister and Madhubani painting for the Dutch Prime Minister, showcasing India's rich artistic heritage.
Australia's controversial tennis star Bernard Tomic has been labelled as the 'king of the excuse' by his country's media after he pulled out of the Rome Masters citing illness and excessive heat.
Carlos Alcaraz said he was eager to get his socks dirty on clay again as the World No. 1 returned to his preferred surface in Monaco this week to build momentum for his French Open title defence.
Novak Djokovic scraped over his first hurdle at the Rome Masters.
Sania Mirza and her Swiss partner Martina Hingis won their first ever title on red clay, capturing the Internazionali BNL d'Italia trophy.