If you find yourself doing things like this regularly it may be worth investigating the object-oriented interface to matplotlib. In your case:
import matplotlib.pyplot as plt
import numpy as np
x = np.arange(5)
y = np.exp(x)
fig1, ax1 = plt.subplots()
ax1.plot(x, y)
ax1.set_title("Axis 1 title")
ax1.set_xlabel("X-label for axis 1")
z = np.sin(x)
fig2, (ax2, ax3) = plt.subplots(nrows=2, ncols=1) # two axes on figure
ax2.plot(x, z)
ax3.plot(x, -z)
w = np.cos(x)
ax1.plot(x, w) # can continue plotting on the first axis
It is a little more verbose but it's much clearer and easier to keep track of, especially with several figures each with multiple subplots.