They first attacked each other on job creation and moved on to healthcare, The New York Times reported. Neither spent much energy on President Barack Obama in the early stages of the debate.
Romney led in most polls until Perry entered the race.
The debate at the Ronald Reagan Presidential Library and Museum in Simi Valley, sponsored by NBC News and Politico, was the first time Perry and Romney have appeared together since the Texas governor entered the presidential race. U.S. Rep. Michele Bachmann of Minnesota, Rep. Ron Paul of Texas, former Sen. Rick Santorum of Pennsylvania, former House Speaker Newt Gingrich of Georgia, former U.S. Ambassador to China and ex-Utah Gov. Jon Huntsman Jr. and former Godfather Pizza Chief Executive Officer Herman Cain of Georgia also participated.
"Michael Dukakis created jobs three times faster than you did, Mitt," Perry told Romney, citing the former Massachusetts governor and Democratic presidential candidate in 1988.
Romney responded in kind: "As a matter of fact, George Bush created jobs three times faster than you did, Governor."
Bill Whalen of Stanford University's Hoover Institution said Perry would be in the bulls-eye at the debate.
"This is the downside of marching to the front of the pack," Whelan said of Perry, whose surging candidacy is overtaking that of presumptive front-runner Romney in public-opinion polls.
"The focus is on you, the pressure is on you and the bar is raised in terms of performance," especially because Perry is "still a novelty and a novel concept at this point," Whalen told the San Francisco Chronicle.
The debate was Perry's first since entering the 2012 presidential contest last month.
Veteran Republican advertising executive Bob Gardner told the Chronicle Perry, Texas' governor since 2000, needed to "look presidential and try to show he's knowledgeable, not just about job creation, but on foreign policy and other issues."
"That's his task," Gardner said. "He should not be playing good ol' boy from Texas."
Many analysts said all the candidates would likely test the limits of Reagan's famous so-called 11th commandment -- "thou shalt not speak ill of any fellow Republican."
In recent days Paul has warned GOP voters Perry can't be trusted after backing Democrat Al Gore for president, and Perry has said Paul thought Reagan's tenure was so bad he ditched the party.
Perry was a Democrat in 1988, when he served as Gore's Texas campaign chairman.
Huntsman, at or near the bottom of the pack in polls, claims some of his rivals are too "extreme" to be elected.
Romney has swiped at Perry's long tenure as governor by blaming "career politicians" for the nation's financial woes. Perry's campaign said Tuesday Romney, as governor, "failed to create a pro-jobs environment and failed to institute many of the reforms he now claims to support."