The British world number one cruised past teenage Russian qualifier Andrey Rublev 6-3, 6-0, 6-2 and will play American Sam Querrey in the third round.
Murray, who is chasing his first Australian Open title after losing five finals, raised concerns in the third set when he went over on his right ankle, grimacing in pain.
Murray looked worried, hobbling noticeably, and was heard telling his player's box "not good news... It's not good".
"I don't know how bad it is. It just is a little bit stiff just now. It's okay. I don't think I've done too much damage," he said afterwards.
"I heard a few sort of little crackles, and it was sore. It was throbbing for the rest of the match. I was moving fine on it, though.
"I'll see how it feels when I get up in the morning. It can sometimes swell overnight."
It allowed the Scot to reach the third round in Melbourne for the ninth straight year and he has yet to drop a set after wins over Illya Marchenko and Rublev.
Murray said he played better than he did against Marchenko on Monday.
"I did pretty good tonight. It was better than the first match. I was hitting the ball a bit cleaner," he said.
"I was hitting through the court more. More winners. I was able to get myself up to net more. I served way better, too.
Murray is looking to become the first man in the Open era to win a Grand Slam title after losing five finals at a single Slam.
He finished as runner-up to Roger Federer in 2010, and to Novak Djokovic in 2011, 2013, 2015 and 2016.
The Scot is also trying to avoid becoming the first man in the Open era to lose six Grand Slam finals at any one major.
His coach Ivan Lendl is the only other man to have lost five finals at any one Slam event -- falling in the title match at the US Open in 1982-84 and 1988-89, but winning the tournament in 1985-87.
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