LiPo battery protection circuits
There are plenty ready-made battery protection boards sold worldwide. 

Check the battery specification for the minimum allowable voltage. Your link does not provide datasheet, so when you place your order, you should ask the seller for the datasheet before buying any battery. 

Select the protection board by its overdischarge cut-off voltage. It needs to be slightly higher than battery's recommended cut-off. Talking about this kind of batteries +/-0.1V matters. 

The other parameter is short circuit protection of the board. Check your Pi Zero, but I think it will consume less than 2A, so everything over that value is OK.

The third parameter is the maximum voltage (overcharge cut-off). Your charger should take care of that, but to be sure check this parameter between board specs and battery specs.