Libertarian Jim Higgins also participated in the debate, held at the annual convention of the Missouri Press Association.
Nixon, who became governor in 2009 after serving 16 years as Missouri attorney general, said that since he signed his first jobs bill into law three years ago, Missouri's unemployment has "been below the national average."
"We're beginning to make progress," Nixon said. "It's built on a solid rock of fiscal discipline, holding the line on taxes and focusing on industries where we can make a difference."
He added, "We're headed in the right direction, and we need to keep moving that way."
State employment figures released this week showed there were 17,900 more workers employed in Missouri in August than in July, putting the state among the nation's top gainers for the month. The jobless rate in Missouri was 7.2 percent, lower than the national rate of 8.1 percent.
However, the civilian labor force -- which counts the number of people who have a job or who are out of work but actively seeking a job -- declined by nearly 11,000.
Spence, a former CEO of Alpha Packaging who is running for office for the first time, used that figure to paint a far less rosy picture of Missouri's economy, comparing the Democratic governor to the captain of the Titanic.
"I feel like we're running into an iceberg in this state," Spence said.
He said Missouri is 50th in the nation in job creation, then ticked off a list of ideas that he thinks could kick-start the economy, including changing the worker compensation system and making Missouri a "right to work" state, where union dues can't be collected as a condition of employment.
Higgins said the state needs to abolish business tax credits, which he called "welfare for the rich."
On education, Nixon touted investment in K-12 schools that was higher than at any point in the state's history. But he acknowledged that the foundation funding formula for public schools is still $500 million below the level it was supposed to be this year.
Asked about allowing vouchers for public school students to attend a private or parochial school, Nixon called the idea "bad public policy," arguing that it takes the state's limited resources and shifts it to the private sector.
"Radical ideas like vouchers just won't work," Nixon said, later adding, "I just think it's a clear values issue. We should not take public dollars and send them to private schools."
Spence agreed to a degree, saying that implementing a voucher program would be "chaos."
"But the only way to improve schools is competition," he said. "Those kids deserve better."
Throughout the debate, Spence repeatedly came back to the argument that he was an outsider and that the governor is a "career politician" that operates at the behest of his big campaign contributors.
What the state needs, Spence argued, is a new CEO.
"The real world is about results. In the real world, this CEO would be fired," Spence said, referring to Nixon.
But Nixon countered that any attempt to paint him as an political partisan or ideologue is inaccurate.
"People know how independent I am. I've been at this a while," he said.
Standing before a crowd of newspaper reporters, editors and publishers, Spence also criticized the media, contending that while small publications have treated him fairly, the same could not be said for "the two large metro papers" -- referring to The Kansas City Star and the St. Louis Post-Dispatch.
"Major newspapers, there's probably a reason they're getting smaller," Spence said.
Nixon's campaign said Spence's attitude toward the media stems from a summer in which the media reported on "the multiple scandals, gaffes, lies and missteps that have plagued his campaign from day one."
The candidates clashed on issues such as business regulations, funding for higher education and the expansion of Medicare.
The only thing all three candidates agreed on was that they oppose increasing the state's tobacco tax, although Nixon said ultimately the issue will be decided by voters this fall as a ballot issue.
The debate concluded a week in which both major candidates took to the airwaves to attack each other.
Spence was first with an television ad linking Nixon to President Barack Obama's federal stimulus.
Nixon struck back with an ad pointing out Spence's ties to a St. Louis bank that has not repaid a $40 million federal bailout loan.
So far, no other debates have been scheduled.