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Another seeded player exited in the demanding conditions, with British number nine Johanna Konta exiting 6-4, 7-5 at the hands of 123rd-ranked lucky loser Bernarda Pera of the US.
Sharapova worked for 80 minutes on the showcase Rod Laver arena to pull out victory, saving herself from a third set with a winning tiebreak effort to close out victory.
The Russian converted five of six break points and will wait for a third-round opponent as Croatian Donna Vekic plays 2016 titlewinner Angelique Kerber.
"Our last match (Beijing first round last October) was three hours," 2008 Melbourne winner Sharapova said of Sevastova. "When she broke me back today in the second set, I though we had another three-setter in store.
"She's a tough opponent with a tricky game no matter the conditions,. I knew I had to get off to a good start. I'm pleased to go two sets on a day like this."
Sharapova lost to the Latvian in the US Open fourth round and then faced her again in her next match played a month later in the Chinese capital.
"I wanted to get through today and I'm really glad that I did. I'm motivated to win," five-time grand slam champion Sharapova said.
Sharapova worked for 80 minutes on the showcase Rod Laver arena to pull out victory, saving herself from a third set with a winning tiebreak effort to close out victory.
The Russian converted five of six break points and will wait for a third-round opponent as Croatian Donna Vekic plays 2016 titlewinner Angelique Kerber.
"Our last match (Beijing first round last October) was three hours," 2008 Melbourne winner Sharapova said of Sevastova. "When she broke me back today in the second set, I though we had another three-setter in store.
"She's a tough opponent with a tricky game no matter the conditions,. I knew I had to get off to a good start. I'm pleased to go two sets on a day like this."
Sharapova lost to the Latvian in the US Open fourth round and then faced her again in her next match played a month later in the Chinese capital.
"I wanted to get through today and I'm really glad that I did. I'm motivated to win," five-time grand slam champion Sharapova said.
