The Indo-Belarussian pair beat Argentina's Martin Garcia and Sebastian Prieto at Flushing Meadows.
The top seeds beat Gaston Etlis and Martin Rodriques of Argentina in straight sets.
The Indo-Belarussian pair will play Wayne Black and Kevin Ulyett in the penultimate round of the BNP Paribas ATP Masters tournament.
Sixth-seeded Paes and Damm knocked out the Czech pair 6-1 6-2.\n\n
The third seeds were shocked by 16th seeds Julian Knowle of Austria and Nenad Zimonjic of Serbia and Montenegro in the men's doubles third round at Wimbledon.
India's Rohan Bopanna and Belarussian partner Max Mirnyi reached the doubles final of the St Petersburg Open defeating Mikhail Mertinak of Slovakia and Lovro Zovko of Croatia 7-5, 6-2 in St Petersburg on Saturday.
They bowed out of the Lyon Grand Prix ATP tennis championship in France.
The second seeds went down to Wayne Black and Kevin Ulyett in the Pacific Open ATP Tennis Masters.
The Indo-Belarussian pair, who won the US Open doubles crown last year, are the top seeds at the Estoril event.
Top seeds Max Mirnyi and Daniel Nestor captured a second successive French Open doubles title by beating American twins Bob and Mike Bryan 6-4, 6-4 in the final on Saturday.
The duo were trailing 5-4 in the first set against American brothers Bob and Mike Bryan when rains disrupted their Masters Cup tennis match.
The fourth seeds got a walkover after their opponents Rainer Schuettler of Germany and Mikhail Youzhny of Russia did not turn up.
American twins Bob and Mike Bryan beat top seeds Jonas Bjorkman of Sweden and Belarussian Max Mirnyi in the final at the US Open.
Indian tennis ace Mahesh Bhupathi and his Belarussian partner Max Mirnyi reached their third ATP World Tour final of the year together, beating fifth seeds Lukasz Kubot and Oliver Marach in straight sets in the Cincinnati Masters Tennis Tournament.
The Indo-Belarussian pair beat the Argentine duo of Gaston Etlis and Martin Rodriguez to keep their hopes of qualifying for the semis of the ATP Masters.
The Indo-Belarussian pair lost to Arnaud Clement and Sebastian Grosjean in the second round at the Miami Masters.
India's Mahesh Bhupathi and his Belarussian partner Max Mirnyi crashed out of Wimbledon after a shock defeat at the hands of Robert Lindsted of Sweden and Horia Tecau of Romania in the men's doubles third round in London.
A Men's doubles Grand Slam title has eluded Mahesh Bhupathi since 2002 and the Indian tennis star is hoping to end the seven-year drought next season when he rejoins forces with Max Mirnyi.
The Indo-Belarussian pair rallied to beat Slovakia's Karol Kucera and Australia's Todd Perry in the second round at the French Open.
Britain's grass season claimed its first ATP tour victims when seeds Julien Benneteau, Lee Hyung-Taik and Fernando Verdasco fell.
Rohan Bopanna and his Belarussian partner Max Mirnyi overcame a second-set lapse to advance to the semifinals of $ 1,049,000 St Petersburg Open.
The top seeds lost to seventh seeds Gaston Etlis and Martin Rodriguez of Argentina in the quarter-finals of the Monte Carlo Masters.\n\n
India's Mahesh Bhupathi on Monday advanced to the second round of the ATP World Tours Finals after he and his partner Max Mirnyi defeated Lukasz Kubot and Oliver Marach in straight sets at London.
The second seeds lost to the French pair of Fabrice Santoro and Michael Llodra in the quarter-final of the men's doubles.
The third seeds thrashed Croatian pair of Mario Ancic and Ivan Ljubicic 6-2, 6-2 in the French Open doubles event.
Swede Jonas Bjorkman and his Belarussian partner Max Mirnyi won the Masters Cup doubles title with a 6-2 6-4 victory over on Mark Knowles and Daniel Nestor on Sunday.
Meanwhile Prakash Amritraj and Hyung-Taik Lee of Korea made a tragic exit, retiring midway through their first round doubles match.
The pair beat the Czech Republic duo of Frantisek Cermak/Leos Friedl in the semi-finals.
Defending champions Leander Paes and Lukas Dlouhy have been seeded third for the men's doubles at the French Open. They open their campaign against Swede Johan Brunstrom and Jean-Julien Rojer of the Netherlands.
Fourth seeds Mahesh Bhupathi and Max Mirnyi overcame a late resistance from Arnaud Clement and Nicolas Mahut to advance to the second round of the men's doubles event of the US Open at Flushing Meadows in New York.
Leander Paes and Martina Hingis eased into the mixed doubles pre-quarterfinals of the Wimbledon championships but it was curtains for Rohan Bopanna and his Spanish partner Maria Jose Martinez Sanchez.
Richard Gasquet celebrated his 19th birthday by winning final of the Nottingham Open
They were beaten in men's doubles quarterfinal of the Nasdaq-100 Open tennis tournament in Miami.
Daniel Nestor of Canada and Elena Likhovtseva of Russia claimed the mixed doubles title at the Australian Open.
Bhupathi and partner Max Mirnyi kick-start their preparations for the year's last Grand Slam with the Tennis Masters Series, starting on Monday in Montreal.
Bhupathi and partner Max Mirnyi advanced to the second round in the ATP Tennis Masters while Paes and Divid Rikl lost in the first.