Combine sugar, milk, butter, and corn syrup in a saucepan over low heat; stir until sugar dissolves. Bring to a boil, then lower heat and simmer for 5 minutes.
Meanwhile, melt marshmallows in the top of a double boiler, melt the marshmallows with the water.
Stir melted marshmallows into the hot syrup mixture until no streaks remain. Remove from the heat and stir in vanilla.