SPRINGFIELD, Mass. — In a display of political muscle, Elizabeth Warren overwhelmingly won the state Democratic Party’s endorsement on Saturday for the United States Senate seat held by Scott P. Brown, a Republican. With the size of her victory, she avoided a party primary in September. Ms. Warren, whose campaign had appeared to be flailing over the past month under questions about her American Indian heritage, won 95.7 percent of the vote of the 3,500 delegates attending the state party convention here. Because the only other Democrat running, Marisa DeFranco, failed to capture 15 percent of the vote, Ms. DeFranco lost the chance to mount a primary challenge.