India's N Sriram Balaji and his Austrian partner Neil Oberleitner, who entered the Australian Open men's doubles draw as an alternate pair, bowed out in the second round.
French veteran Richard Gasquet was also among eight men given wild-card entries.
One of the rising stars of the men's tour, Fonseca shocked ninth seed Andrey Rublev on his Grand Slam main draw debut at the Australian Open in January and became the youngest Brazilian to win an ATP tournament at the Argentina Open the following month.
Interestingly, it was also in the US Open where Rohan Bopanna competed in his maiden Major final way back in 2010 along with Pakistani partner Aisam-ul-Haq Qureshi.
Three-time champion Novak Djokovic battled past Frenchman Corentin Moutet in a match that lasted more than three hours on Thursday.
World No 1 Novak Djokovic was beaten by Tomas Machac in the Geneva Open semi-finals.
Herbert and Mahut added to their 2018 French Open title after recovering from a shaky start.
India had mixed fortunes at the US Open on Friday. Rohan Bopanna advanced to the men's doubles second round partnering Denis Shapovalov, but Leander Paes, teaming with Guillermo Duran, made a first-round exit.
The Indian has won five ATP Masters 1000 titles with five different partners, although he has never won a major championship in men's doubles. Not bad for someone whose knees lack cartilage.
With the victory, Herbert and Mahut added the Melbourne Park title to their US Open, Wimbledon and French Open crowns to complete the career Grand Slam.
Pierre-Hugues Herbert and Nicolas Mahut became the first all-French duo to win the U.S. Open men's doubles title after easing past Britain's Jamie Murray and Australian John Peers 6-4, 6-4 on Saturday.
India's Rohan Bopanna, partnering Australia's Matthew Ebden advanced to the semi-finals of the men's doubles at the US Open tennis tournament, at Flushing Meadows, New York, on Tuesday. The sixth seeds scored a 7-6(10), 6-1 victory over the 15th seeded American combination of Nathaniel Lammons and Jackson Withrow in the quarter-finals.
Andy Murray returned to the All England Club in the men's doubles on Thursday and eased into the second round with French partner Pierre-Hugues Herbert.
Fourth seed Grigor Dimitrov survived a scare against Pierre-Hugues Herbert before holding his nerve to win 3-6, 6-2, 6-4 in the second round of the Monte Carlo Masters on Tuesday, while Dominic Thiem edged out Russian youngster Andrey Rublev.
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.
World No 96, Bhambri lost 3-6, 6-7 (3-7), 5-7 to Herbert in a match that lasted nearly two and half hours.
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 have been drawn in Group Ashe-Smith along with John Peers/Jamie Murray and Simone Bolelli/Fabio Fognini.
The 32-year-old three-time Grand Slam champion has not played singles since losing in the Australian Open first round in January.
Indian tennis stars Sania Mirza and Leander Paes will battle it out for the French Open mixed doubles title with their respective partners, having won their semi-final matches on Thursday.
The American duo won 5-7, 6-1, 13-11 as they added the season-ending crown to the Wimbledon and US Open titles.
Nicolas Mahut and Pierre-Hughes Herbert won the Wimbledon men's doubles title after a straight sets win over fellow French duo Julien Benneteau and Edouard Roger-Vasselin on Saturday.
Sharan and Nys did not get any break-point in the 72-minute clash
The Murray bothers last played together at the 2016 Rio Olympics, and were a prolific partnership when Britain won the Davis Cup in 2015.
The second seed pair of Leander Paes and Daniel Nestor suffered a shock quarter-final defeat against the French pair of Nicolas Mahut and Pierre-Hugues Herbert to crash out of the ATP Topshelf Open in 's-Hertogenbosch.
Nicolas Mahut and Pierre-Hughes Herbert became the third home duo to win the French Open men's doubles when they beat second seeds Oliver Marach and Mate Pavic 6-2, 7-6(4) on Saturday.
David Goffin put the visitors ahead by beating Lucas Pouille in the opening singles before Jo-Wilfried Tsonga levelled for 1-1 when he defeated Steve Darcis in the second singles on Friday.
Davis Cup holders Britain edged into a 2-1 lead in Serbia after Jamie Murray and Dominic Inglot won Saturday's doubles.
Indian Aces continued their dominance in IPTL 2 with a 25-18 win over Japan Warriors on the opening day of tournament's Dubai leg on Monday.
Rohan Bopanna and Florin Mergea saved a match-point before emerging winners, while Sania Mirza and Martin Hingis were also tested en route to the quarter-finals of the ATP/WTA Western and Southern Open, in Cincinnati, on Thursday.
Jo-Wilfried Tsonga beat Dusan Lajovic 2-6, 6-2, 7-6(5), 6-2 to give France an unassailable 3-1 lead against Serbia and book their place in the Davis Cup final.
Simone Bolelli and Fabio Fognini became the first all Italian pair to win a grand slam men's doubles title in almost 60 years when they beat Frenchmen Pierre-Hughes Herbert and Nicolas Mahut 6-4 6-4 at the Australian Open on Saturday.
Former World No 1 Roger Federer returned from a 10-week layoff with a 6-3, 6-4 second-round victory against Spain's Guillermo Garcia Lopez at the Monte Carlo Masters on Tuesday.
Nick Kyrgios, who retired injured from Wimbledon on Monday, knew he was struggling with a hip injury even as he came out on court but he wanted to give his favourite tournament a shot.
India's Sumit Nagal gave a mighty scare to three-time Grand Slam winner Stan Wawrinka by taking off the first set but then wilted under pressure to bow out of the Prague Open in the quarter-finals on Thursday.
Already without the likes of Richard Gasquet and Gael Monfils for the final against Croatia, Noah decided to leave out Lucas Pouille, the top-ranked player in his squad.
Bhambri, ranked 116 in the world, had reached the second round when the ATP 250 event was played in Chennai in January 2017.
Defending champions Rohan Bopanna and Jeevan Nedunchezhiyan were ousted from the Tata Open Maharashtra but Yuki Bhambri and Divij Sharan combined to shock the top seeds, keeping the Indian hopes alive, in Pune, on Thursday.
Britain's Jamie Murray and Brazil's Bruno Soares will end the year as the top-ranked doubles duo after French pair Nicolas Mahut and Pierre-Hugues Herbert lost at the ATP World Tour Finals on Friday.
With the American men experiencing their longest US Open title drought in the Open era, Venus Williams led the American charge into round two on Monday with a 6-3, 3-6, 6-2 win over Viktoria Kuzmova of Slovakia.
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