But voters defeated measures that would have hired more police officers and raised salaries for public school teachers. A measure to double funding for certain youth programs appears to have passed.
Kaplan will succeed veteran City Councilman Henry Chang, who has been on the council since 1994.
Kaplan got 62 percent of the vote, easily defeating school board member and Bay Area Rapid Transit district planner Kerry Hamill, who got 37 percent of the vote.
Kaplan and Hamill engaged in a runoff because they were the top two finishers in a five-person contest in the June primary election, with Kaplan garnering 39.3 percent of the vote and Hamill getting 21.6 percent.
Kaplan said on her Web site, "In order to achieve many of the other important goals for our city, and provide the basic building blocks for a thriving community, we must first provide for public safety in Oakland."
Measure NN, a parcel tax that would have asked property owners to pay $107 a year initially to hire 105 new police officers and 75 additional police service technicians, got 55 percent of the vote but fell far short of the two-thirds majority it needed to pass, according to complete unofficial election results.
The tax, which was put on the ballot by Mayor Ron Dellums and a majority of the City Council but opposed by council president Ignacio De La Fuente, would have grown to $177 the second year and $267 a year in the third and fourth years.
Measure N, which would have taxed people $120 a year to increase salaries for teachers in an effort to attract and retain them, got 61.5 percent of the vote but appears to have fallen short of the two-thirds majority it needed for approval.
It was put on the ballot by Vincent Matthews, the state's administrator for the Oakland Unified School District.
A controversial provision in the measure called for 15 percent of the money that's raised to be given to charter schools.
Measure OO, which will more than double city funding for certain youth programs by 2011, won by a margin of 53 percent to 47 percent. It only needed a simple majority to pass.
The measure doesn't provide a new revenue source for the increased spending, so opponents said that because the city already faces a budget deficit of at least $42 million, the measure will hamstring the city's ability to provide essential services for seniors, families and children.
Supporters included school board president David Kakishiba, Olis Simmons, the executive director of Youth UpRising, and the Rev. George Cummings, the co-chair of Oakland Community Organizations.
Opponents included Dellums, De La Fuente, Fire Chief Daniel Farrell and Helen Hutchinson, the president of the League of Women Voters of Oakland.