It is Roger Federer's first time back at the summit since October 2012 having first claimed the top position in February 2004.
Haase, 26, explained in the daily Volkskrant that, after undergoing the test, he received a letter from the ATP advising him "to get a lawyer" and indicating that he would have to undergo three more tests in the following two weeks.
The second-seeded German, won also won the event 12 years ago, maintained his slim chance of qualifying for next month's ATP finals in London.
Tipsarevic has had a dreadful run this season as he has slipped out of the top 10 in a downward trend which has accelerated over the last four months.
Djokovic dropped his serve to fall behind 2-1 in the opening set but broke back immediately and took control from there against his 32-year-old opponent.
The third seed, playing his first Grand Slam match since winning the US Open, won 6-3, 6-1, 6-3 in 1hr 37min on Rod Laver Arena.
The 20-year old 217-ranked Bhambri had his chances, especially in the first set when he held breakpoints against Haase who himself allowed the Indian to hold serve in the third game after leading 40-0.
Juan Martin del Potro defeated Slovenian qualifier Grega Zemlja 7-5, 6-3 on Sunday to win his first title at the Austrian Open and improve his standing in the race to the year-end championships.
Marinko Matosevic of Australia rallied to defeat sixth-seeded Robin Haase of the Netherlands 1-6, 6-3, 6-2 on Monday in the opening round of the Erste Bank Open.
A singles win from Roger Federer gave Switzerland the decisive point to stay in the top tier of the Davis Cup after taking an unassailable 3-1 lead over the Netherlands Sunday in the best-of-five playoff fixture.
Roger Federer and Stanislas Wawrinka slumped to a 6-4, 6-2, 5-7, 6-3 defeat to Robin Haase and Jean-Julien Rojer on Saturday as the Netherlands stayed alive in their Davis Cup World Cup play-off with Switzerland.
World number one Roger Federer and his 2008 Olympic gold medal partner Stanislas Wawrinka put Switzerland 2-0 up in their Davis Cup World Group play-off against the Netherlands in damp conditions on Friday.
Sixth seeds Mahesh Bhupathi and Rohan Bopanna moved into the men's doubles quarterfinal here at the Cincinnati Masters tennis after receiving a walkover.
French Open dangerman Juan Martin Del Potro shrugged off a knee injury scare as well as sweltering 30-degree heat to reach the French Open second round on Sunday.
Veteran Czech Radek Stepanek on Tuesday ended the Madrid Masters run of Australian Bernard Tomic in the first round, with the Queensland youngster exiting 6-2, 7-5.
Juan Martin del Potro celebrated the start of his pre-French Open campaign with a 6-1, 6-0 hammering of Portugal's Rui Machado to reach the quarter-finals of the Estoril Open on Thursday.
Sixth-seeded Robin Haase recovered from a shaky first set to beat Simone Bolelli 6-3, 6-2 Monday and advance to the second round of the Estoril Open.
Australia's Bernard Tomic bowed out of the Barcelona Open in the second round on Wednesday after losing a marathon battle to Spanish clay specialist Albert Montanes 6-0, 5-7, 7-5.