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.
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.
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.
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.
Federer has not played in the French Open for the last two years in order to give rest to his body and focus on other events where he has greater chances of winning.
The second-ranked Spanish star hasn't played since retiring in the quarterfinals of the Australian Open in late January.
The sixteen-time grand slam champion was slated to face fellow Spaniard Feliciano Lopez in the opening round of the tournament on Wednesday.
In the Sportsman of the Year category, Federer waved off tough competition from the likes of Rafael Nadal and Cristiano Ronaldo to bag the honours.
The Swiss star first became world number one in February 2004 and had not topped the rankings since October 2012 before reclaiming it again in Rotterdam.
It should be noted that Federer has won the tournament seven times, which accounts for the most number of Dubai Championships title lifted by any player.
It's been more than five years since Federer held the No. 1 ranking, and 14 years since he first reached the top spot.
Roger Federer revealed that though his goal was to make it to the semi-finals as he wanted to become the oldest man to seal a numero-uno spot, he somehow managed to lift the title.
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.
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.
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.
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.
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.
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