Federer can equal his season-best start of 16-0 with a win in the quarterfinals, where he will meet Chung Hyeon of South Korea in a rematch of their Australian Open semifinal.
It has been a great tournament for Bhambri, who knocked out players of the calibre of two-time doubles Grand Slam winner Nicolas Mahut and world number 12 Lucas Pouille en route the third round.
Wozniacki blew a 3-0 lead in the first set and was on the run most of the match before losing for the second time this year to Daria Kasatkina.
Flach reached No. 1 in the men's doubles rankings and paired with Robert Seguso to form one of the world's top teams in the 1980s.
Venus Williams defeated sister Serena 6-3, 6-4 in the third round for her first win over her younger sibling since 2014.
In a stunning performance, the 110th ranked Yuki, who qualified for the main draw, dispatched the ninth seed Frenchman 6-4 6-4 in one hour and 19 minutes.
It was yet another disappointing return for the 30-year old as he admitted that he was out of sorts while playing in just his second event of 2018.
Federer, who earned his fifth title at Indian Wells last year, saved a set point in the second-set tiebreaker and advanced to face Filip Krajinovic on Monday.
Serena leads Venus 17-11 all-time and has won eight of their last nine meetings, most recently the Australian Open final last year.
Paes has returned to Top-50 and is placed 46 in the rankings after his stupendous show at the ATP 500 event in Dubai where he ended runners-up.
Sharapova announced the mutual parting with Sven Groeneveld on Friday, two days after she was beaten in straight sets by Naomi Osaka of Japan in her return to Indian Wells.
Williams' only competitive appearances since the birth came in December at an exhibition in Abu Dhabi, a Fed Cup doubles match with sister Venus last month and an exhibition in New York on Monday.
In his opening round in the main draw, Yuki will fight it out with fellow qualifier Nicolas Mahut, ranked 101, and if he manages to cross the first hurdle he will be up against world number 12 Lucas Pouille.
Sharapova's ranking of No. 41 in the world forced her to play a first-round match in the tournament she has won twice. A failed doping test led to a 15-month ban for the five-time major winner.
Yuki, seeded ninth, edged past America's Dennis Novikov 7-5, 7-5 while Ramkumar defeated Michael Mmoh 6-3, 7-5 in his first-round match in the qualifiers on Wednesday.
Serena, a winner of 23 Grand Slam titles, is in the same quarter of the draw as older sister Venus, the siblings could potentially face each other in the third round of the tournament.
Federer emerged from the tunnel of smoke and walked onto the court greeted by roars and thousands of camera phones held high for the first Bay Area appearance of his career.
The Williams sisters were the headliners Monday night in the Tie Break Tens tournament in Madison Square Garden, an eight-woman event in which all matches were 10-point tiebreakers, instead of the usual games and sets.
Paes, who reached the final in Dubai with Jamie Cerretani last week, jumped to 46, two places behind Divij Sharan (44), who gained one place, while, Rohan Bopanna remains unchanged at number 20.
The 29-year-old Argentine star beat three straight players ranked ahead of him in the hard-court event, topping No. 6 Dominic Thiem in the quarterfinals, No. 5 Alexander Zverev in the semifinals and eighth-ranked Anderson in finals.
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