Combine water, brown sugar, orange juice, cinnamon stick, ginger, orange zest, salt, cloves, and allspice in a medium saucepan; bring to a boil. Reduce heat and simmer until sugar is dissolved, 3 to 5 minutes.

Stir in cranberries and return to a boil over medium heat. Cook until cranberries start to burst and mixture thickens slightly, 8 to 10 minutes; sauce will thicken further upon cooling.

Transfer cranberry sauce to a bowl; remove and discard cinnamon stick. Store in the refrigerator until serving.