"It's such a special feeling. I love playing back here," said 31-year-old Wozniacki. "Last year I had some special memories and just to be able to be back out here on Rod Laver Arena is something extremely special and emotional."
The Dane beat Simona Halep in the 2018 final to claim her first Grand Slam title. When Federer edged past Marin Cilic in the men's showdown on the same court the following day, it was his 20th major championship.
"I'm very happy with the first round. It's been great," said the 37-year-old Swiss after his seventh win in as many matches against Istomin. "I'm going to try everything possible to win the title again."
Second seed Rafael Nadal ended his 2018 season early to have surgery on a foot injury. He showed few aftereffects in his straight sets win over the Australian James Duckworth.
"It is not easy to come back after a lot of months, especially against a player playing super aggressive on every point," said Nadal, who won the title in 2009."
Angelique Kerber, the second seed in the women's event, signalled her intent to add to her 2016 title with a 6-2, 6-2 demolition of the unseeded Slovenian Polona Hercog.
Another former champion, Maria Sharapova, was even more ruthless. It was 6-0 6-0 against 22-year-old Harriet Dart from Britain.
Playing in her 15th Australian Open, Sharapova, who won in 2008, said she was pleased to advance to the second round so rapidly.
"I'm still working through some painful days," added the 31-year-old Russian who suffered a thigh injury at the Shenzen Open in China just before the Australian Open.
"But I felt like I did all the right things in order to get through the match."