Defying predictions that their participation would be lackluster, Latinos turned out in record numbers on Tuesday and voted for President Obama by broad margins, tipping the balance in at least three swing states and securing their position as an organized force in American politics with the power to move national elections.

Over all, according to exit polls not yet finalized by Edison Research, Mr. Obama won 71 percent of the Hispanic vote while Mitt Romney won 27 percent. The gap of 44 percentage points was even greater than Mr. Obama’s 36-point advantage over John McCain in 2008.

After waiting in long lines in countless places — more than four hours at some South Florida polls — Latinos had such a strong turnout that it lifted them to 10 percent of voters nationwide, an increase from 6 percent in 2000. Latino leaders said their voters had cast ballots that ensured Mr. Obama’s relatively narrow plurality — fewer than 2.8 million votes — in the popular count.

“Latino voters confirmed unequivocally that the road to the White House passes through Latino neighborhoods,” said Clarissa Martinez De Castro, a top official at NCLR, the Hispanic organization also known as the National Council of La Raza, which joined in an extensive campaign this year to register and turn out voters.