Matplotlib: draw grid lines behind other graph elements
According to this - http://matplotlib.1069221.n5.nabble.com/axis-elements-and-zorder-td5346.html - you can use Axis.set_axisbelow(True)
(I am currently installing matplotlib for the first time, so have no idea if that's correct - I just found it by googling "matplotlib z order grid" - "z order" is typically used to describe this kind of thing (z being the axis "out of the page"))
To me, it was unclear how to apply andrew cooke's answer, so this is a complete solution based on that:
ax.set_axisbelow(True)
ax.yaxis.grid(color='gray', linestyle='dashed')
If you want to validate the setting for all figures, you may set
plt.rc('axes', axisbelow=True)
or
plt.rcParams['axes.axisbelow'] = True
It works for Matplotlib>=2.0.