The figure for Mr. Obama is backed up by a national exit poll for media organizations that showed him winning 49% of the Cuban-American vote in the state. By comparison, he captured 35% of that vote four years ago. In 2004, Democrat John Kerry received 29% of the state’s Cuban-American vote, and in 2000, Democrat Al Gore won 25% of it.

The surprising development, given Cuban-Americans’ traditionally staunch support for the GOP, could help reshape U.S. policy toward Cuba.

Given his overwhelming support among Florida’s non-Cuban Hispanic voters, who make up a growing share of the electorate, Mr. Obama carried the state’s Latino vote overall by 61% to 39%, exceeding his margin in 2008 by seven percentage points. Together, both trends are accelerating a realignment of the state’s Latino vote, from once solidly Republican to now reliably Democratic, analysts say.