The USC/Los Angeles Times poll found Garcetti with a 21-point lead among conservative voters: He led Greuel 54% to 33%.
Curiously, he was leading her in other parts of the political spectrum, too, but with smaller margins: Garcetti was ahead 45 to 44 among moderates and 50 to 43 among liberals, the poll said.
In fact, Garcetti was leading Greuel on her home turf in the San Fernando Valley, 47% to 43%, the poll said.
The USC/Los Angeles Times survey reveals a quick change in fortunes for the two candidates.
A week before that poll, Greuel and Garcetti were in a virtual tie, according to the Edmund G. "Pat" Brown Institute of Public Affairs at California State University, Los Angeles.
The electorate gave the institute a vivid assessment of the two candidates.
"More voters say that Garcetti, by a slight margin, will be the better candidate in providing leadership and fighting crime, while voters prefer Greuel for handling education and as a candidate who 'cares about people like me,'" the institute said.
"The most cited negative by likely voters against Greuel is that she is too close to special interests and unions, and the most noted criticism of Garcetti is that he cannot be trusted," the institute added.
Among the biggest issues in the mayoral race is the role of unions and their campaign spending.
Greuel is receiving big financial support from unions representing city employees. Most of those unions have put their money on her, including about $1.5 million from the local representing workers at the city's Department of Water and Power.
The cost of city jobs are part of the budget crisis that awaits the new mayor, who will have to help negotiate salary agreements with the water department, police, fire, and other city employees.
To help the city balance its budget, Garcetti has backed layoffs, furloughs and an increase in the retirement age for new city workers. A few unions have endorsed Garcetti, but their money is a fraction of what Greuel has received.
Greuel has criticized Garcetti for proposing draconian measures against labor.
In response, Garcetti calls his opponent "the DWP's mayor" and asks voters: "How much will it cost you?"
Voters will render their verdict on the two candidates on Tuesday.