Dr Jones told the council how her local library had played an important part in her early education and highlighted the importance of the buildings in low socio-economic communities such as Greerton.
"If you turn your back on 40,000 people in one of the lowest socio-economic communities in this city the consequences will be far reaching," she said.
"I urge you to be a visionary council and to provide vital services to this community."
Mr Molloy told the council the "cave people of Tauranga" had made debt out to be the "boogeyman" when it just signalled a fast-growing city struggling to cope with the needs of its people.
"Base your decision on what is good for your community and get this over the line."
All councillors except Rick Curach, Catherine Stewart and Gail McIntosh voted for the inclusion.
Mrs Clark said she was elated and relieved by the decision.
"This is not over though, this is a good start but it is not the end.
"We will keep fighting for this until it gets across the line, we are so close now I can feel it."
Supporters would be rallying outside the Greerton Library during the draft Annual Plan process, Mrs Clark said.
"Once again we are hearing the same old arguments for why this should not go ahead but the community is determined.
"We will be helping people fill out submissions to make sure this gets through this time."
Friends of the Library, as a registered charitable trust, can apply for the estimated $250,000 design funding, Mrs Clark said.
If successful the library upgrade is expected to take about 18 months to complete with a temporary library to be set up in the Greerton Hall.