AMES, Iowa — Donald J. Trump, who is rarely at a loss for words, admitted “I don’t know what’s going on” when confronted by Ben Carson’s surge past him in early-voting Iowa, where Mr. Trump had led the Republican presidential field for months.

Mr. Trump has derided Mr. Carson for lacking the vigor and fortitude to be president, but voters here are drawn to the retired neurosurgeon’s low-pitched manner.

“That smile and his soft voice makes people very comforted,” said Miriam Greenfield, a farmer in Jewell, Iowa.

In an election season that has confounded party leaders and experts, the rise of Mr. Carson is another unexpected twist. His supporters cite Mr. Carson’s character, not his positions, as the main reason they back him. And they say his low-key approach is precisely what would tame Washington’s bitter partisanship, rather than Mr. Trump’s swagger.