Sharing a debate stage for the first time, the five candidates for governor who will appear on the Nov. 4 ballot talked education, transportation and energy during a one-hour exchange of ideas that featured one flare-up.

Republican Charlie Baker, Democrat Martha Coakley and independents Evan Falchuk and Jeff McCormick convened for a forum at Faneuil Hall last week and a forum in Cambridge earlier in the day, but their appearance at CityStage was their first with Scott Lively, an anti-gay Springfield preacher who steered a question about infrastructure financing toward his wheelhouse of religiosity.

"We really need to be looking at the moral infrastructure of Massachusetts as well," Lively said. "We're killing unborn babies every single day in this state. We are promoting sexual perversion to children in the public schools. Those kinds of things are corrupting us from the inside much worse than what's happening with our road system and our bridges."

"I just want to say, Scott, that was kind of a veiled reference, I think, to gay people. And as the brother of a gay man who lives and is married in Massachusetts, I just want you to know that I found that kind of offensive," Baker said to applause, after answering a different question.

"I believe in the bible, Charlie. I'm sorry that you don't," Lively shot back.

The candidates otherwise did not directly engage with Lively, as Coakley touted the benefits of early education, McCormick discussed repealing the state's inventory tax and Falchuk criticized the political establishment.

"Everybody in the political establishment today will say all the right things about how important it is to educate kids, especially in early childhood education. But the money isn't there. The money isn't there," Falchuk said, noting lawmakers passed a $1 billion bill financing the expansion of a convention center. He asked, "The only question is why do the people we elect not actually take action to deal with this issue? Why don't they?"

Noting that a 2016 ballot question will likely propose legalizing marijuana for recreational use, Falchuk critiqued lawmakers on that issue, saying they should "hold hearings like adults do." With inaction in the Legislature voters at the ballot box decriminalized possession of less than an ounce of marijuana in 2008, and legalized medical marijuana in 2012.

Moderator Jim Madigan quizzed the candidates about global warming and a proposed Kinder Morgan natural gas pipeline, leading from the New York border to Dracut, which would ease the winter shortfalls of the fuel that heats homes and provides electricity.

Coakley said she didn't think the Kinder Morgan pipeline "as it is formulated" is the "right solution," and Falchuk said he, too, opposes the pipeline. McCormick said the state should "expand the capacity of our existing natural gas pipelines," which follow a different route, and Baker said the state should have prepared for the current natural gas shortfall years ago, a process that could have included increased capacity along the existing pipeline. Lively was the only global warming disbeliever, calling global warming "nonsense," and saying, "Most of what's happening is related to the sun."

On the cost of higher education, Baker advocated three-year degrees in public higher education, extolled the merits of online learning for people juggling responsibilities aside from school, and called for co-op learning based on the Northeastern University program that places students in career settings.

"We need to invest in K through 12 and make sure our kids are getting extended learning time, the computer science they need - I know we all talked about that today - so they have science, engineering, technology and math, and how about a little arts and music - and I always get a big round of applause when I say recess, because I liked recess when I was a kid," said Coakley.

Falchuk said he wanted to make community college free for two years. Coakley said community colleges should have "need-blind" admissions, while Lively said he wouldn't increase funding, saying those on stage with him shared a "liberal big government perspective - perhaps not Mr. McCormick."

"I think that was an endorsement. Did anyone else hear that?" McCormick said, calling for "strong" charter schools and noting the importance of vocational schools.

On growing the economy in western Massachusetts, McCormick called for a doubling of the tax credit available for work on historic structures and the creation of "enterprise zones." Coakley discussed completing a theater renovation in Holyoke and educational investments, while Baker and Falchuk noted the differences in the area's economy. Falchuk said work on a rail line from Hartford, Conn., into Vermont would help the corridor, and Baker said he would sit down with mayors to hear their priorities.

"I don't have to spend my first year meeting with mayors around Massachusetts. I've been doing that during this campaign," Coakley said later. Coakley, who was first elected attorney general in 2006, also knocked Baker, the state's former budget writer, for the financing of the Big Dig project, burying Interstate 93. She said, "When I came in as attorney general we had to deal with the financing issues around the Big Dig, under the Baker administration with Governor Weld."

Baker talked about the possibility of public-private partnerships for transportation infrastructure projects, and Falchuk advocated tolls at the borders, suggesting past Massachusetts governors have been reluctant to extract state revenues from the first-in-the-nation presidential primary voters to the north.

"No one does that. I think part of it is that historically all of our governors have been busy trying to run for president, and they're looking at New Hampshire and saying, 'I don't want to tax those guys,'" Falchuk said. "I do."