Undead Fortitude. If damage reduces the zombie to 0 hit points, it must make a Constitution saving throw with a DC of 5 + the damage taken, unless the damage is radiant or from a critical hit. On a success, the zombie drops to 1 hit point instead.
Actions
Morningstar. Melee Weapon Attack: +6 to hit, reach 5 ft., one target. Hit: 13 (2d8 + 4) bludgeoning damage.
RollQuest summary Condition immunities: poisoned. Senses: darkvision 60 ft., passive Perception 8. Languages: understands Common and Giant but can't speak. Saving throws: Wis +0. Speed: 30 ft.
RollQuest ships the D&D 2014 SRD as a content pack, on a 5e character sheet that does the maths - roll from the sheet and let the numbers work themselves out. Free to start.