To get around the outage, iiNet recommended users set their DNS to use a publicly available service such as Cloudflare's 184.108.40.206 service. Other users have said setting DNS to use Google's 220.127.116.11 also works.
iiNet added that engineers were investigating the issue.
Users that were seeking information from TPG had no luck, as the site was been intermittent and failing to load during the outage.
Just before 2:30pm, services were restored.
"There was an issue inside the network which has been resolved," TPG said as a technical summary of the issue.
"Engineers have identified the issue, and have restored services. TPG apologises for any inconvenience."
TPG said on Twitter the outage affected all its customers, and hit internet as well as home phone services.
iiNet was more forthcoming and said users that had applied manual DNS settings could revert to automatic DNS.
Updated at 2:54pm AEDT, 29 January 2020: Added resolution of issue and TPG explanation.