However, the American struggled at the beginning of the match, losing four games in the first set before she got a grip on the match and secured the victory.
Keys is ranked ninth in the WTA singles rankings, compared to Olijnykova, who is ranked 92nd.
"I'm so happy to be back in Melbourne. Obviously I was very nervous at the beginning," Keys said, according to AFP.
In her next match, Keys will play compatriot Ashlyn Krueger on Wednesday night, local time in Sweden.
Corrected: In an earlier version of the text, the wrong days were stated for the matches.
