The contest is among the closest – and most closely watched – in the nationwide battle over who will control the Senate following elections in November.
Ms. Warren, a financial-law expert known for aligning with populist concerns about Wall Street banks, garnered 47 percent support in the Suffolk University/7News poll, released late Wednesday night. The Democrat's tally was just a hair behind Senator Brown, who had 48 percent of likely voters behind him.
Back in February, the poll found 49 percent for Brown and 40 percent for Warren. The share of respondents saying they were undecided has fallen from 9 percent in February to 5 percent in the new poll, taken earlier this week.
Warren appears to have solidified her position despite controversy that has emerged in recent weeks over whether she inappropriately identified herself as a "minority" law scholar and whether that self-identification may have advanced her career.
Warren has said she did not seek any hiring preferences based on her heritage, which she has said includes traces of Cherokee and Delaware Indian ancestry. But she self-identified as a "minority" in a national directory of law professors in the 1980s and early 1990s, a time that included her arrival on the faculty of the prestigious Harvard Law School.
Voters in Massachusetts so far do not view the controversy as a major issue, the Suffolk University poll found. When asked, "Do you think Warren's Native American heritage listing is a significant story," nearly 7 in 10 said no.
The poll revealed some other issues that may be important as the campaign season rolls forward. Although Massachusetts has a track record of voting Democratic, Brown enjoys a high favorability rating as a moderate Republican.
Some 58 percent of state voters cite a favorable view of Brown, who was a lawyer serving in the Army National Guard before entering politics and winning a special Senate election in 2010, after the death of Sen. Edward Kennedy. Warren's favorability rating is 43 percent, an improvement of eight percentage points since the February poll.
A majority of Bay State voters also said it's helpful to have one Republican senator, as well as one Democrat. (The state's other Senate seat is held by Democrat John Kerry.)
Warren has been seeking to tar Brown as an ally of Wall Street and as an obstacle to needed banking reforms. So far those efforts haven't dragged Brown down significantly. When asked, "Do you believe a vote for Scott Brown is a vote for Wall Street?," only 33 percent in the poll said yes.
On Thursday, both candidates pushed again on familiar themes. Warren called for further strengthening of bank regulation, citing the investment losses that JPMorgan Chase has recently experienced from its exposure to credit derivatives. Brown's campaign released a statement that Warren herself has an accountability problem, on the questions about minority status.
On that issue, 49 percent of voters polled said they believe Warren is telling the truth about her claims to be part native American, while 28 percent don't believe she is. Forty-one percent said they believe Warren benefited from listing herself as a minority, while 45 percent say they don't think she benefited.
Much about Warren's record on this issue is unclear, and therefore its influence on the campaign remains fluid. Some of the people involved in hiring her have stated that the issue of minority status didn't come up in the decision. But documents related to her hiring at several universities have not been released, and her hiring at Harvard came at a time when the law school was under pressure to diversify its faculty.
Also, the question of whether Warren has verifiable Indian ancestry hasn't been resolved.