Wrap cinnamon sticks, cloves, and allspice berries in a spice bag.

Combine cranberries, water, and spice bag in a medium saucepan over medium heat. Cook until cranberries begin to burst, about 10 minutes.

Stir in sugar and reduce the heat to low. Continue cooking until sugar dissolves, about 5 minutes. Remove from the heat and let cool to room temperature, about 30 minutes.

Remove and discard spice bag. Cover cranberry sauce and chill in the refrigerator before serving, 8 hours to overnight.