Makarova, who reached the Australian Open semi-finals after stunning Serena Williams three years ago, rode an early break for a 5-3 lead and, even though her Latvian opponent got back to 5-5, raced away with the first set tiebreak.
Third seed Ostapenko, who also lost her opening match in Shenzhen last week, put up a fierce fight at the start of the second set but faded after losing her first service game and Makarova moved on to face Barbora Strycova or Daria Kasatkina.
"It was first match of the season so of course I was nervous at the beginning," said Makarova.
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"But I tried to stay solid, to stay with my aggressive game, and it worked in the important moments."
With temperatures in western Sydney well above the 40 degrees Celsius mark, some withdrawals might have been expected and local Ellen Perez progressed when France's Kristina Mladenovic retired at 6-4 4-2 down.
German seventh seed Julia Goerges also withdrew from the tournament citing a knee injury having won the Auckland Classic earlier in the day.
Venus Williams, Garbine Muguruza and Johanna Konta, the reigning champion, are all also in a strong women's field at Sydney's Olympic Park.
In the men's draw, twice former champion Viktor Troicki went out in the first round 6-3 6-7(3) 7-5 at the hands of unorthodox Ukrainian Alexandr Dolgopolov.
(Reporting by Nick Mulvenney, editing by Amlan Chakraborty)
