Powering two devices with a Li-Ion battery
I see couple of issues:  

Are you powering the Pi Zero bypassing the on board regulator?
3.7 V can damage the processor and on board chips which run at 3.3 V   

If you are not bypassing--> the on board regulator will have a drop out voltage and may fail to provide you the 3.3 V necessary for normal operation of the Pi .