Defending champion Caroline Wozniacki comfortably through
Boulter defeated Ekaterina Makarova in her opener in Australia, and she broke her opponent in the opening game in front of a supportive Australian crowd.
Aryna Sabalenka will face Amanda Anisimova in the third round
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But Sabalenka showed her renowned intensity on court to wrestle control and take the first set with a flurry of thunderous forehands.
The Brit was copeting in the second round of a Grand Slam for only the second time in her career, and she was in danger of being broken early in the second set but produced three cracking points to hold serve in the first game.
But in her next service game, Sabalenka challenged a long call on her way to the crucial breakthrough.
Boulter continued to push her opponent all the way with one sweeping backhand raising hopes of breaking back, but Sabalenka held her nerve to serve out the match.
The performance was another indication of Boulter's huge promise, but the result means that Johanna Konta is the only remaining Briton in the singles draws, with the world number 37 facing Garbine Muguruza in her second-round contest on Thursday.