Council also killed a measure for the so-called "revenue neutral" tax assessments, which would have required the city to lower the tax rate in any year that reassesses raised overall property values in the city.
"We want to be fiscally prudent but also make strategic investments, so I think it's a good budget," Council President Darrell Clarke said.
Expanding the homestead exemption was the key sticking point, those involved in negotiations said.
The exemption currently eliminates the first $40,000 of a home's assessed value for tax purposes if the owner resides there. Councilman Brian O'Neill had proposed increasing that to $50,000, but Kenney administration officials thought the cost, an estimated $30 million per year, was too high.
The administration and council agreed on an expansion to $45,000.
"We think that's probably a good level for the homestead exemption at this point," said the mayor's chief of staff Jim Engler. "And we're happy to see that council approves of almost all of the investment we proposed in this year's budget."
Council, sitting as the Committee of the Whole, also approved a capital budget and a five-year spending plan.
But it declined to vote on the "revenue neutral" measure, also proposed by O'Neill in response to widespread dissatisfaction with increases in property assessments, a process that city officials have admitted was flawed.
Councilmembers seemed skeptical of the approach, noting it would grant tax relief even to those whose assessment hadn't increased and those who could afford the increase, rather than targeting homeowners who struggled to keep up with taxes in parts of the city that are gentrifying.
Even O'Neill seemed to lose enthusiasm for the proposal after finance director Rob Dubow testified that the bill would cost the city more than $300 million and the school district $400 million over the next five years.
"That would force the district back into the painful days of deciding what programs to cut, depriving our students of the resources they need and likely reversing the progress the district has made over the last several years," Dubow said.
O'Neill said Council should work in the future on a plan that would allow homeowners to have faith in the assessment process.
"The public," he said, "is convinced revenue raising plays a big part in it."