DES MOINES, Iowa—Mitt Romney pulled out a razor-thin victory by just eight votes in the Iowa caucuses, edging out Rick Santorum and opening the Republican primary season with a dose of momentum going into a New Hampshire primary he is heavily favored to win.

Mr. Santorum's performance was in some ways more remarkable, as the former Pennsylvania senator vaulted to the top just weeks after he had been little more than a footnote in the race. By effectively tying Mr. Romney, he made at least a tentative case for himself as the...