The WBUR poll gives her 45 percent support to Brown's 40 percent support. Only 12 percent of voters say they are undecided.

It seems that Warren's campaign message is sticking with voters, too — she argues on the stump that she's the better candidate for the middle class and average Massachusetts voters, and she's seen as the candidate who "best understands the needs of middle-class families" and the one who "will stand up for regular people when in the Senate."

However, Brown retains his lead in likability — 52 percent of likely voters say they have a favorable opinion of him compared to 48 percent who have a favorable view of Warren. And this poll shows him posting more crossover appeal: He's pulling 15 percent of Democrats from Warren. Brown also has a 14-percentage-point lead among independent voters, significant in a state where over 50 percent of voters are unaffiliated with a party.

The poll was conducted among 507 likely Massachusetts voters from Sept. 15-17 and has a margin of error of plus or minus 4.4 percentage points.