diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 9747fd46ad0..1cafb620c76 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -99,6 +99,8 @@ Bug fixes
   (:issue:`3402`). By `Deepak Cherian <https://github.com/dcherian/>`_
 - Allow appending datetime and bool data variables to zarr stores.
   (:issue:`3480`). By `Akihiro Matsukawa <https://github.com/amatsukawa/>`_.
+- Fix plotting with transposed 2D non-dimensional coordinates. (:issue:`3138`)
+  By `Deepak Cherian <https://github.com/dcherian>`_.
 
 Documentation
 ~~~~~~~~~~~~~
diff --git a/xarray/plot/plot.py b/xarray/plot/plot.py
index 2acc8ddd452..33955038ba1 100644
--- a/xarray/plot/plot.py
+++ b/xarray/plot/plot.py
@@ -698,10 +698,22 @@ def newplotfunc(
 
         # check if we need to broadcast one dimension
         if xval.ndim < yval.ndim:
-            xval = np.broadcast_to(xval, yval.shape)
+            dims = darray[ylab].dims
+            if xval.shape[0] == yval.shape[0]:
+                xval = np.broadcast_to(xval[:, np.newaxis], yval.shape)
+            else:
+                xval = np.broadcast_to(xval[np.newaxis, :], yval.shape)
 
-        if yval.ndim < xval.ndim:
-            yval = np.broadcast_to(yval, xval.shape)
+        elif yval.ndim < xval.ndim:
+            dims = darray[xlab].dims
+            if yval.shape[0] == xval.shape[0]:
+                yval = np.broadcast_to(yval[:, np.newaxis], xval.shape)
+            else:
+                yval = np.broadcast_to(yval[np.newaxis, :], xval.shape)
+        elif xval.ndim == 2:
+            dims = darray[xlab].dims
+        else:
+            dims = (darray[ylab].dims[0], darray[xlab].dims[0])
 
         # May need to transpose for correct x, y labels
         # xlab may be the name of a coord, we have to check for dim names
@@ -711,10 +723,9 @@ def newplotfunc(
             # we transpose to (y, x, color) to make this work.
             yx_dims = (ylab, xlab)
             dims = yx_dims + tuple(d for d in darray.dims if d not in yx_dims)
-            if dims != darray.dims:
-                darray = darray.transpose(*dims, transpose_coords=True)
-        elif darray[xlab].dims[-1] == darray.dims[0]:
-            darray = darray.transpose(transpose_coords=True)
+
+        if dims != darray.dims:
+            darray = darray.transpose(*dims, transpose_coords=True)
 
         # Pass the data as a masked ndarray too
         zval = darray.to_masked_array(copy=False)
diff --git a/xarray/tests/test_plot.py b/xarray/tests/test_plot.py
index 730bf335dc8..e44ad2a5164 100644
--- a/xarray/tests/test_plot.py
+++ b/xarray/tests/test_plot.py
@@ -270,6 +270,7 @@ def test2d_1d_2d_coordinates_contourf(self):
         )
 
         a.plot.contourf(x="time", y="depth")
+        a.plot.contourf(x="depth", y="time")
 
     def test3d(self):
         self.darray.plot()
@@ -2156,6 +2157,34 @@ def test_yticks_kwarg(self, da):
         assert np.all(plt.gca().get_yticks() == expected)
 
 
+@requires_matplotlib
+@pytest.mark.parametrize("plotfunc", ["pcolormesh", "contourf", "contour"])
+def test_plot_transposed_nondim_coord(plotfunc):
+    x = np.linspace(0, 10, 101)
+    h = np.linspace(3, 7, 101)
+    s = np.linspace(0, 1, 51)
+    z = s[:, np.newaxis] * h[np.newaxis, :]
+    da = xr.DataArray(
+        np.sin(x) * np.cos(z),
+        dims=["s", "x"],
+        coords={"x": x, "s": s, "z": (("s", "x"), z), "zt": (("x", "s"), z.T)},
+    )
+    getattr(da.plot, plotfunc)(x="x", y="zt")
+    getattr(da.plot, plotfunc)(x="zt", y="x")
+
+
+@requires_matplotlib
+@pytest.mark.parametrize("plotfunc", ["pcolormesh", "imshow"])
+def test_plot_transposes_properly(plotfunc):
+    # test that we aren't mistakenly transposing when the 2 dimensions have equal sizes.
+    da = xr.DataArray([np.sin(2 * np.pi / 10 * np.arange(10))] * 10, dims=("y", "x"))
+    hdl = getattr(da.plot, plotfunc)(x="x", y="y")
+    # get_array doesn't work for contour, contourf. It returns the colormap intervals.
+    # pcolormesh returns 1D array but imshow returns a 2D array so it is necessary
+    # to ravel() on the LHS
+    assert np.all(hdl.get_array().ravel() == da.to_masked_array().ravel())
+
+
 @requires_matplotlib
 class TestDataArrayGroupByPlot:
     @requires_cftime