EASTON—The three candidates vying for the Republican nomination in the US Senate special election faced off in their first debate Tuesday night in a lively exchange before a crowd of about 300 that showcased the candidates’ divergent profiles.

Michael J. Sullivan, who previously served as US Attorney and director of the US Bureau of Alcohol, Tobacco, Firearms and Explosives, played the relaxed senior statesman, unruffled by any questions tossed his way. He shrugged off a Globe story about his campaign manager repurposing policy statements used last election cycle for the website of congressional candidate Richard R. Tisei.

“There’s nothing on there that I would say that contradicts positions that I’ve taken publicly,” Sullivan said during the forum at Stonehill College. “It’s hard for me to be critical of the people who are volunteering and trying to be helpful.”

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State Representative Daniel B. Winslow, of Norfolk, who has also served in the Romney administration and as a judge, portrayed himself as an outsider who would shake up the status quo.

“If you think things are going well, vote for the other guys, because I’m here to try to change things in Washington,” he said, panning sequestration as an example of the problems and deriding Democrats for “scare tactics.”

Gabriel E. Gomez, a 47-year-old private equity investor from Cohasset, was the halting newcomer leaning heavily on his life story as the son of Colombian immigrants who spent years as a US Navy SEAL.

“We cannot send another career politician down to D.C.,” Gomez said, repeating the descriptor he used at least a half-dozen times during the debate.

All three committed to serve no more than two terms, if elected, though Winslow, 54, and Sullivan, 58, said it would be difficult to impose a term limit on members of Congress.

None of the three candidates supported an assault weapons ban to contain gun violence, though Gomez advocated stricter background checks, particularly for the mentally ill.

“People like to think that bans are effective,” said Sullivan. “They’re completely ineffective. I’ve seen it from my experience.”

Asked about US Senator Rand Paul’s filibuster over civil liberties on the floor of the Senate last week, Winslow said he spoke out in support of him even as it was happening.

“When the civil liberties of the US citizens were at stake where were the Democrats?,” he asked. “Where was Steve Lynch? Where was Ed Markey? It was left to one senator and I was proud to stand with him in spirit. I hope to stand with him on the floor.”

On immigration, Gomez noted that as the son of immigrants, he favors a pathway to citizenship that would be “not easy but also not impossible.”

Winslow called for a comprehensive approach to immigration reform, sealing off porous borders, speeding up the process for those seeking to immigrate legally, and expediting the deportation of those who commit crimes. Neither he nor Gomez called for amnesty for any particular group of illegal immigrants.

Sullivan, on the other hand, said he would give amnesty to undocumented immigrants who had served the United States in the military.

Gomez, asked about his effort to persuade Democratic Governor Deval Patrick to appoint him senator in the interim, after John F. Kerry left the seat vacant to become secretary of state, said he would release on Wednesday the letter he sent seeking the appointment.

Asked about whether they would work with freshman US Senator Elizabeth Warren on prosecuting banks, Gomez demurred, saying he could work with anyone.

“I don’t believe that any bank or any institution is too big to fail or too big to prosecute,” he said.

Winslow criticized federal prosecutors for targeting some for justice, and not others, specifically pointing to US Attorney Carmen M. Ortiz’s prosecution of Internet activist Aaron Swartz on federal hacking charges—a prosecution that has been seen by some critics as overly aggressive.

“There has to be some sense of proportion, some sense of balance in our prosecutorial decisions and I think that’s where the senate in a role to play,” said Winslow.

But Sullivan stood up for prosecutors, saying that individuals, not corporations, commit crime.

“Do we prosecute a company just for the sake of saying we’re tough and have [innocent] people lose their jobs?” Sullivan said. “Senators should be making the law, the courts should be interpreting it.”

Later, asked whether Ortiz went too far in her prosecution of Swartz, who took his own life, Sullivan said there were situations during his leadership of the same office when suspects awaiting trial committed suicide.

In this case, he said, “What we learned from the media was suggested it might have been heavy-handed, but we don’t know certainly all the facts,” he said. “We’re not privy to all the evidence Carmen Ortiz might have had.”

Winslow said the government should “reexamine our criminal laws and shift some of the discretion away from prosecutorial authorities perhaps back to the courts.”

Gomez said, “The thing that alarms me is the potential politicization of a department such as US attorney,” and he called it “just another example of why people don’t trust careers politicians down in Washington D.C.”

The event was hosted by Peter Ubertaccio, director of the Martin Institute at Stonehill College, and cosponsored by GateHouse MA/WickedLocal, WCVB (Channel 5), and WGBH radio.