diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index ea9bb7a2c228..61b161642fef 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -2272,7 +2272,14 @@ def handle_single_axis(scale, autoscaleon, shared_axes, interval,
             # ignore non-finite data limits if good limits exist
             finite_dl = [d for d in dl if np.isfinite(d).all()]
             if len(finite_dl):
+                # if finite limits exist for atleast one axis (and the other is infinite), restore the
+                # finite limits
+                x_finite = [d for d in dl if (np.isfinite(d.intervalx).all() and (d not in finite_dl))]
+                y_finite = [d for d in dl if (np.isfinite(d.intervaly).all() and (d not in finite_dl))]
+
                 dl = finite_dl
+                dl.extend(x_finite)
+                dl.extend(y_finite)
 
             bb = mtransforms.BboxBase.union(dl)
             x0, x1 = getattr(bb, interval)
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 49b6a57e67ac..86b6f2a3ddc2 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -5134,3 +5134,18 @@ def test_minorticks_on(xscale, yscale):
     ax.set_xscale(xscale)
     ax.set_yscale(yscale)
     ax.minorticks_on()
+
+
+def test_twinx_knows_limits():
+    fig, ax = plt.subplots()
+
+    ax.axvspan(1, 2)
+    xtwin = ax.twinx()
+    xtwin.plot([0, 0.5], [1, 2])
+    # control axis
+    fig2, ax2 = plt.subplots()
+
+    ax2.axvspan(1, 2)
+    ax2.plot([0, 0.5], [1, 2])
+
+    assert((xtwin.viewLim.intervalx == ax2.viewLim.intervalx).all())