Attorney General Martha Coakley has the early advantage in the governor’s race, a new WBUR poll shows.

The survey gives Coakley a 39-29 lead over Republican front-runner Charlie Baker.

Her lead is built, in large part, on support from women voters, who have played a pivotal role in recent statewide elections.

“She is doing very well among, particularly, women over the age of 50,” said Steve Koczela, president of The MassInc Polling Group, which conducted the survey for WBUR.  “They really are responding to what she has to say and have a very positive view of her so far.”

The poll of 504 registered voters shows Coakley with a 17-point edge over Baker among women.

But Baker leads among women — and leads overall — in head-to-head matchups with four other Democrats vying for the governor’s chair.

He tops Treasurer Steve Grossman 33-23. And he holds leads of more than 20 points over three lesser-known candidates: homeland security expert Juliette Kayyem, former Obama administration health care administrator Donald Berwick and biopharmaceutical executive Joseph Avellone.

There are other good signs for Baker, a venture capitalist and former health care executive.

Polls show the Republican was largely forgotten by voters after his failed bid for governor in 2010. But the WBUR survey suggests he is steadily rebuilding name recognition. And voters who have formed judgments have a generally positive view. Thirty-two percent have a favorable opinion of Baker and 14 percent have an unfavorable opinion.

But Jeffrey Berry, a political scientist at Tufts University, cautions that it’s still early.

“At this stage of the race there’s no negative campaigning,” he said. “The Democrats are not really going after [Baker]. They’re more concerned about their own primary.”

It is also early for Coakley, who seems to be benefiting from a sizable name recognition edge over her Democratic rivals — an edge that seems likely to dissipate as the race wins broader public attention.

Just 3 percent of voters say they have not heard of Coakley, compared with 43 percent who say they have not heard of Grossman.

Most voters say they have never heard of the other three Democrats or independents Evan Falchuk, a lawyer and former business executive who is running or governor, and venture capitalist Jeffrey McCormick, who is seriously considering a bid.

Still, for now, the poll offers a measure of redemption for two candidates humbled by 2010 electoral defeats — Baker in the governor’s race and Coakley in her U.S. Senate contest with Republican Scott Brown.

“They say there are no second acts in politics, but the two leaders of this race — at least at this point — are both second acts,” said pollster Koczela.

The poll, which has a margin of error of 4.4 percent, also found Gov. Deval Patrick weathering a series of negative news stories in recent months.

The survey found three in four voters following news about two controversies “very closely” or “somewhat closely”: a chemist who falsified test results in a state drug laboratory and the Department of Children and Families (DCF) losing track of a 5-year-old Fitchburg boy.

A third controversy — problems with the state’s health care website — is not getting the same notice, though nearly one in two poll respondents say they have been following the story.

Voters are split down the middle on the governor’s handling of the three issues, with 38 percent approving and 37 percent disapproving.

But Patrick’s overall job approval ratings are holding up as he enters his final year in office, with 53 percent approving and 39 percent disapproving.

Follow-up interviews with poll respondents found voters voicing broad trust in Patrick, and arguing that he can’t be expected to know the details of what happens in state agencies.

“If he knew about [the problems in the drug lab, at DCF and with the health care website] beforehand and didn’t act that’s one thing,” said Joan Rastani, a retired technology executive active in Democratic politics in Framingham. “But I got the impression that when he found out about them, he took appropriate measures.”

The job approval numbers represent a roughly 10-point drop from Patrick’s fall polling figures. But they still offer succor to a governor trying to remain relevant as he enters his final year in office — and staves off inevitable questions about his lame-duck status.

The WBUR poll also found continued strong support for casino gambling — 53 percent in favor and 39 percent opposed — even after a string of cities and towns rejected casinos.

Anti-casino activists are trying to get a repeal of the state’s gambling law on the ballot. The effort is tied up in court.

Baker, who served in the Weld and Cellucci administrations, tacked to the right during the 2010 gubernatorial race — looking to exploit Tea Party ferment in a move that was widely criticized after the campaign.

He has cast his second gubernatorial run as a return to his more authentic, moderate roots. But if interviews with a handful of WBUR poll respondents are any indication, it’s not an effort that is broadly registering yet.

Those with a favorable view of Baker spoke not of moderation, but of principle.

“He calls it like it is,” said Edward Rauscher, a retired police officer from Ipswich who usually votes Republican and says the government is “too wasteful.”

Christine Qualey, a retired teacher from Abington, also suggested that Baker’s last campaign lingers; she says she was angered by the Republican’s statements on education and would vote for anyone but him in the coming election.

Winning over women appears a vital task for Baker, who lost the female vote by 24 points in the 2010 election, according to a post-campaign poll by The MassINC Polling Group.

Geraldine Marchand, a retired teacher from Blackstone on the Rhode Island border, says she would vote for Coakley over Baker if the election were held today.

But she says she’s open to supporting Baker — particularly if a Democrat other than Coakley emerges from the party’s September primary.

First, though, she needs to learn more about the candidates in a race that’s just begun.

“I would say a good 60 percent of the people in Massachusetts do not know these people running for governor,” she said. “We know Martha Coakley because she’s been in the paper, she’s been on the radio, but we don’t know who’s running against her…We need the information before we can make a good choice.”

MORE: At WBUR.org, find the poll’s topline results and crosstabs