Polls show the two candidates are locked in a tight race. Greuel has gone after Garcetti in campaign ads, questioning his ethics.
At the debate at the Sinai Temple in West Los Angeles, the two clashed when Garcetti criticized Greuel for accepting $3.8 million in support from a Department of Water and Power union.
"I think it's disingenuous, disingenuous to say that you are the independent guy, and he did want their support. He did ask for their support -- DWP and others," said Greuel. "I don't think it's right when you ask for someone's support and they don't give it to you, then you demonize them the next day."
Garcetti clarified by saying that he's not talking about a specific union.
"I'm not demonizing one union or another. I'm saying that this election isn't for sale, that nobody should be able to come in with that amount and to be able to say that a thousand people's voices can be drowned out with one," said Garcetti.
The wide-ranging debate touched on several issues, including city development, Los Angeles International Airport runway construction and the expansion of the Los Angeles Police Department, where, again, the two candidates differed.
"I think, also, it's irresponsible at a time when we're still finishing the balancing of our budget to talk about hiring 2,000 more officers. Miss Greuel called it a plan 15 times when she announced it, next day it was a goal, and back at a debate it was a plan again, so I'm confused whether it's a goal or a plan," said Garcetti.
Greuel defended her stance.
"We are the most under-policed police department in the entire country, in the big cities," she said.
A recent Eyewitness News SurveyUSA poll showed about 13 percent of voters are still undecided.