World number 37 Putintseva exchanged words with the umpire and threw her racket on the court at the end of the first set after incidents involving movement in the corporate boxes and security distracted her.
Home favourite Tomljanovic wrapped up her 7-6 (4) 6-2 success in just under two hours.
World number one Ashleigh Barty who, like Halep, received a first-round bye, awaits Anastasia Pavlyuchenkova after the Russian beat Estonia's Anett Kontaveit 6-2 6-4.
Three-time grand slam champion Angelique Kerber, seeded ninth, overcame China's Wang Qiang 6-1 6-3.
Sofia Kenin of the United States beat Swiss player Viktorija Golubic 6-0 6-4 and Russia's Daria Kasatkina lost 6-4 6-4 against fourth seed Belinda Bencic.
In Monday's other matches, American Danielle Collins beat Belarusian Aliaksandra Sasnovich 6-3 6-2, Latvian Anastasija Sevastova lost 6-4 1-6 3-6 to Croatia's Donna Vekic, and Ukrainian Dayana Yastremska won 7-5 6-3 against Hungary's Timea Babos.
At the Hobart International, British number two Heather Watson battled back from a set down to beat Switzerland's Jil Teichmann.
The 27-year-old won 1-6 6-4 6-4 against the world number 67 in just under two hours and will face Fiona Ferro in the last 16.
French player Ferro progressed after Sweden's Rebecca Peterson retired from their match with the score 4-4 in the first set.
Fifth seed Veronika Kudermetova comfortably beat Australian Samantha Stosur 6-2 6-2, while Polish sixth seed Magda Linette scraped past Russian Svetlana Kuznetsova 7-6 (2) 7-6 (9).
Kristyna Pliskova came from a set down to beat Serbia's Nina Stojanovic 1-6 6-4 6-3, while Slovakian Viktoria Kuzmova also battled back to progress, defeating China's Zhu Lin 5-7 6-2 7-6 (3).
Elsewhere, American Lauren Davis beat Australian Astra Sharma 6-3 3-6 7-6 (6) and Ukraine's Kateryna Kozlova eased through against Spain's Sara Sorribes Tormo, winning 6-2 6-1.
