Federer's third title at the Rotterdam tournament comes a day before he officially returns to the top of the player rankings, more than five years after he was last world number one.
In Sunday's final, the 36-year-old Federer will win his 97th career title if he beats Grigor Dimitrov, dubbed "Baby Fed" early in his career for his style similarities with the Swiss great.
With a win over Robin Haase, the 36-year-old Federer becomes the oldest man to top the ATP world rankings, surpassing Andre Agassi, who held the record at the age of 33.
Bhambri booked his place in the semi-finals after defeating Japan's Yasutaka Uchiyama 5-7, 6-2, 6-4.
The 36-year-old Swiss great already has the record for most weeks as the ATP World Tour's No. 1 player (302) but he has not held the top spot since late 2012.
The 30-year-old had earlier accepted a wildcard entry to make her first appearance at the tournament since 2006.
It was the first win in an ATP tournament for the 21-year-old Dutchman, who dominated the second and third sets against a lacklustre Wawrinka.
With the win, the 25-year-old Indian has now set up a clash against Lee Duck-hee of South Korea for a place in the summit showdown.
Federer began his campaign at the ABN AMRO tournament on Wednesday with a flawless performance, defeating Ruben Bemelmans 6-1, 6-2 in just 46 minutes.
On being asked about who has the potential to be the next Sania, the 31-year-old said that she should not be the benchmark for the upcoming talent.
Federer, 20-time Grand Slam champion, closed to within 155 points of Nadal after his win last month at the Australian Open against world No.3 Marin Cilic of Croatia.
In Serena's first competition since giving birth five months ago, she and sister Venus lost 6-2, 6-3 to Lesley Kerkhove and Demi Schuurs of the Netherlands in a Fed Cup doubles match.
The 112-ranked Bhambri, who qualified for the Australian Open, will be looking for some momentum ahead of the long season, which also includes a Davis Cup tie against China.
Williams teams up with Lauren Davis to face Lesley Kerkhove and Demi Schuurs of the Netherlands in Sunday's doubles match.
Up against a lower-ranked opponent, placed a humble 761 in the WTA list, Karman snapped a four-match losing streak by beating Eudice Chong on Friday.
Federer has the opportunity to become the oldest tennis player to claim the top spot as it was USA's Andre Agassi who currently holds the record as he achieved the feat at the age of 33.
Halep had a grueling time in Melbourne last month, badly twisting her ankle and battling her way through two marathon matches to the final, where she lost to Caroline Wozniacki.
Earlier, the world number one said that he was hoping to make a return from injury at the Mexican Open, beginning February 26.
Sania, winner of six Grand Slam titles, is out of action since October 2017 due to an injury in her right knee, forcing her to miss first Grand Slam of the season.
Germany will play either Britain or Spain in the quarterfinals from April 6-8.
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