With 87 percent of the vote in, Biden had 33.4 percent of the vote, Sanders had 27 percent and Warren had 21.4 percent.
Biden captured the lion's share of support from late-deciding voters. Forty-three percent of voters who made up their minds in the last few days broke for Biden, according to NBC News Exit Poll results.
Exit polls showed Warren trailing Biden and Sanders among both men and women. Warren had 24 percent of the female vote, compared to Sanders' 26 percent and Biden's 34 percent. Only 17 percent of men said they voted for her, compared to 34 percent for Biden and 31 percent for Sanders.
Earlier polls had shown Warren winning in the Bay State, but that changed last week, with Sanders leapfrogging her in a WBUR poll in the wake of his strong showings in New Hampshire and Nevada. Then Biden jumped ahead of both of them on the heels of his commanding win in the South Carolina primary Saturday.
The WBUR poll showed that Sanders' support in the state comes from younger voters, with nearly half of respondents under age 45 saying they'd vote for him.
That held up Tuesday — exit polling showed that 48 percent of voters who said they voted for Sanders were younger than 45.
Warren on Tuesday also lost her birthplace, Oklahoma, where she was in fourth place with 78 percent of the vote in. By midnight, she'd been allocated 13 delegates, bringing her total to 21. That's fewer than those of Pete Buttigieg, who dropped out of the race Sunday.
President Donald Trump celebrated her poor showing on Twitter, saying she was the "loser of the night," along with her billionaire foil, Mike Bloomberg. "She didn't come close to winning her home state of Massachusetts. Well, now she can just sit back with her husband and have a nice cold beer!" he wrote.
Download the NBC News app for breaking news and politics
Speaking Tuesday night at a town hall in Detroit — the Michigan primary is March 10 — Warren didn't sound as if she was going anywhere.
"My name is Elizabeth Warren, and I'm the woman who's going to beat Donald Trump," she told the cheering crowd shortly before the polls closed in Massachusetts. "I'm also going to help take back the Senate and put Mitch McConnell out of a job."
She also made an appeal to voters who say they like her but are worried about her electability.
"Cast a vote that will make you proud. Cast a vote from your heart and vote for the person you think will make the best president of the United States of America," she exhorted.