Some 24% of debate-viewers named Mr. Trump and 23% picked Mr. Rubio as the winner of the eight-candidate event, which was sponsored by the Wall Street Journal and Fox Business News. Ted Cruz and Ben Carson followed, with 13% declaring each to have won.

Mr. Trump’s lead in the Internet survey was larger among debate-watchers who said they’d vote in a Republican primary.

Among those GOP voters, Mr. Trump was declared the winner by 28%, with 23% naming Mr. Rubio. Mr. Cruz followed, with 16%, while Mr. Carson had 14%.