Compared with the vote for President Obama in 2008, Ms. Coakley lost the most ground in the central and southeastern parts of the state. These more sparsely populated areas have traditionally been the most favorable to Republican candidates. Mr. Brown’s campaign resonated with independents who were anxious about the economy, an important factor in these places, which have the state's highest unemployment rates. These towns have also seen their unemployment rates rise the fastest in the last year.

Mr. Brown's victory was a stunning rebuke to the Democratic Party. In every town across the state, the Democratic share of the vote was down from the 2008 presidential election. The towns with the strongest Obama vote did not shift as much to the right the rest of the state, but that may provide little solace for party leaders. These areas tended to be more densely populated and have residents with higher levels of education.

As expected, turnout was depressed for this special election compared with last year’s general election. About 54 percent of registered voters turned out, compared with 73 percent in November 2008. In President Obama’s strongest areas — towns where he received more than 60 percent of the vote — the number of voters was about 30 percent below 2008 levels. In the rest of the state, the number of voters was down just 25 percent. In Boston — one of the strongest areas for Democrats — the number voting fell 35 percent.

Former Gov. Mitt Romney — the last Republican, before Mr. Brown, to win a major statewide election in Massachusetts — succeeded in the 2002 governor’s race by making gains in traditionally Democratic areas while carrying independent voters in the suburbs. Mr. Brown received fewer votes than Mr. Romney in Democratic strongholds like Boston and the surrounding urban areas, but he commanded a larger share of the vote than Mr. Romney in most of the state, especially in areas with a lot of independents.