Mr Brownless said it was important to give the best chance of seeking an additional $1m of external funding, including from the Government's tourism infrastructure fund.
The $1m was needed to up-spec the building to an iconic status by adding the huge roof, lifting the final cost to $5m. Tourism Bay of Plenty was tasked with finding the additional $1m.
Mr Brownless said the Government took $100m a year in GST from tourism and the council received nothing.
"It is time the Government sent some of that money from GST back to the regions."
Councillor Larry Baldock led the move back to the council funding $4m, saying there were issues of reputation and relationships that would have far-reaching implications and financial consequences for the city.
''We should try and correct the mistake made on June 8. It was an unplanned, ill-conceived knee-jerk reaction that had not been thought through properly."
He succeeded with a compromise funding solution to shift the project's funding burden in the 2018-19 financial year more towards the city's economic development rate funded by commercial ratepayers.
This year's $500,000 contribution to the project would be funded equally from the general rate and the economic development rate. But instead of the remaining $3.5m being equally funded, the council agreed that 70 per cent should come from the economic development rate in 2018-19.
This bigger contribution by the city's commercial ratepayers would be subject to public consultation in the draft 2018-28 Long Term Plan.
Councillor Steve Morris, who opposed spending $4m, said it was great proposal but the council could not have everything.
There were discretionary items coming up as part of the Long Term Plan including rebuilding Coronation Pier on the downtown waterfront, the Memorial Park to The Strand walkway, lighting Matapihi rail bridge and sirens at the Mount and Papamoa.
Councillor Rick Curach said the visitor information centre started out as a $1.3m to $1.8m project when it was first discussed last year and then doubled in a short space of time.
"You get a lot of people with vested interests attempting to capture the council.''
He wanted to see what a design and build procurement process would come up with using $2.5m plus $1m to make the building iconic.
Supporters of the $4m were Mayor Greg Brownless and councillors Larry Baldock, Leanne Brown, Kelvin Clout, Max Mason, and Terry Molloy. Opposing were Rick Curach, Bill Grainger, Gail McIntosh, Steve Morris and Catherine Stewart.
The decision was welcomed by Tourism Bay of Plenty. Chief executive Kristin Dunne said a purpose-built visitor information centre would reinforce the city's reputation as a leading tourism destination and would service about 500,000 visitors a year.
"With over three million visitors per annum and over 99 cruise ships forecast next season, we need a large facility that can safely and warmly welcome our guests, tell the stories of tangata whenua, promote local businesses and be pride of place for the Bay of Plenty."
Proposed funding split for visitor information centre
Tauranga commercial ratepayers: $2.7m
Tauranga general rate: $1.3m
External funding: $1m