Playing his first match since injuring his knee at Indian Wells last month, Nadal showed no signs of rust as he raced into a 5-0 lead in the first set on Court Rainier III.
Kyrgios was due to play Spain's Roberto Bautista Agut in the first round in Rome, but was replaced by lucky loser Alexandr Dolgopolov in the men's draw.
Mensik said that the physio worked on his knee and deemed that it was not a serious problem.
In the evening session, men's third seed Alexander Zverev and women's fourth seed Jessica Pegula were forced off the court mid-match due to rain and the threat of lightning.
Second seed Coco Gauff overcame early problems on serve to cruise past China's Wang Xinyu 6-3, 6-2, keeping her composure despite eight double faults in the first set to book a meeting with Ukraine's Dayana Yastremska in the third round.
Rafael Nadal returned to Roland Garros after his birthday celebrations and showed no signs of slowing up, railroading compatriot Roberto Bautista Agut 6-1, 6-2, 6-2 in the fourth round on Sunday.
Bhambri, ranked 116 in the world, had reached the second round when the ATP 250 event was played in Chennai in January 2017.
'I have so much to look forward to in 2021, including the Olympics'
Tsitsipas will play 22nd-seeded Spaniard Roberto Bautista Agut for a place in the semi-finals.
Sanam Singh beat Roberto Bautista-Agut of Spain to enter the pre-quarter-finals of the boys' singles at Wimbledon.
Medvedev outlasts Zverev to reach Halle final
Spain's talisman Rafael Nadal sealed a sixth Davis Cup title for his country on Sunday when they beat Canada 2-0 in the final of the revamped event.
India's top singles tennis player Somdev Devvarman has been handed a direct entry in the main draw of the ATP Chennai Open tennis tournament after Estonia's Jurgen Zopp pulled out of the event due to a back injury.
World number two Rafael Nadal has been named in Spain's squad for their Davis Cup World Group quarter-final against Germany in Valencia next month.
Battle-scarred Argentine Juan Martin del Potro clinched his 21st career title with a 6-4, 6-4 win over Kevin Anderson in the Mexican Open final in Acapulco on Sunday.
American Frances Tiafoe celebrated his 21st birthday by stunning Bulgaria's Grigor Dimitrov 7-5, 7-6(6), 6-7(1), 7-5 in the fourth round of the Australian Open on Sunday.
Carlos Alcaraz, who advanced to the last eight in Cincinnati for the third time, has now won 36 of his last 38 matches.
Rafael Nadal has been left out of Spain's Davis Cup squad for their World Group first-round match against Croatia this weekend due to fatigue.
Former world number one Novak Djokovic's preparation for next month's Australian Open suffered a blow after he pulled out of the season-opening exhibition event in Abu Dhabi on Friday due to pain in his right elbow.
Stefanos Tsitsipas said that his victory in the final of the Mallorca Championships on Saturday was a major milestone in his career as the Greek claimed his maiden grasscourt title leading up to Wimbledon next week.
France, who were 2-0 up courtesy of Arthur Rinderknech and Adrian Mannarino, faced little resistance from Ecuador as wins for Benjamin Bonzi and the doubles pair of Pierre-Hugues Herbert and Nicholas Mahut secured victory for the 10-times champions.
Norrie's semi-final opponent will be another American, fourth-seeded Tommy Paul, who crushed Stefan Kozlov 6-3, 6-1 in an all-US matchup.
Novak Djokovic proved to be a calming influence throughout
Roger Federer survived a stern test from Spain's Roberto Bautista Agut to reach the Miami Open quarter-finals on Tuesday, while top-seeded Swiss compatriot Stanislas Wawrinka was eliminated on his birthday.
Spain hope new world number one Carlos Alcaraz will be ready for their Davis Cup tie
The 32-year-old three-time Grand Slam champion has not played singles since losing in the Australian Open first round in January.
Marin Cilic completed a dream week by steering Croatia into the Davis Cup World Group on Sunday but Spain found themselves out in the wilderness after crashing to defeat in Brazil.
Roger Federer reached the Rogers Cup semi-finals on Friday after coming to the net early and often in a straight sets victory over Roberto Bautista Agut on a windy day in Montreal.
Novak Djokovic and Roger Federer notched up contrasting victories to reach the Shanghai Masters quarter-finals on Thursday while David Ferrer fought back from a set down to knock out Andy Murray.
The 45th ranked Kyrgios came back from a set down to beat Serbia's Laslo Djere 5-7, 7-6(1) 7-6(1) on Tuesday and was scheduled to play Spaniard Roberto Bautista Agut next.
Brothers Elias and Mikael Ymer comfortably won their singles rubbers against Canada as seven-times champions Sweden made a roaring start in the Davis Cup Finals in Madrid on Thursday.
World number one Ash Barty delighted the Memorial Drive crowd by breezing through to the Adelaide International semi-finals with a comfortable 6-3, 6-4 victory over Sofia Kenin on Friday.
Rafael Nadal has withdrawn from next week's season-opening exhibition event in Abu Dhabi due to ongoing fitness problems, the world number one said.
Yuki Bhambri and his New Zealand partner Michael Venus registered a straight sets victory on their Grand Slam debut, but Divij Sharan's Australian Open campaign ended in the first round, in Melbourne, on Wednesday.
Bryan said he had not advised Murray either way but hoped he would get the surgery to at least improve his quality of life.
PHOTOS from day four of the Wimbledon championships at the All England Lawn Tennis and Croquet Club in London on Friday.
Defending champion Stanislas Wawrinka survived some anxious against Gilles Muller before proceeding into the men's singles semi-finals at the ATP Chennai Open tennis tournament.
Second seed and world number 14 Roberto Bautista Agut outclassed Benoit Paire in a lop-sided semi-final to set up the singles title clash of the ATP Chennai Open with young Daniil Medvedev, who rallied to reach his maiden ATP final, in Chennai on Saturday.
World number one Novak Djokovic is on verge to become the first man to win US$100 million in prize money as he aims to book his place in the quarter-finals of the French Open for the 10th time.
Italy's Matteo Berrettini beat Brazil's Joao Fonseca to give his side a flying start and Matteo Arnaldi then outlasted Thiago Monteiro to put the hosts into a 2-0 lead.
