diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index d8d3382675e..828a66db6ab 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -24,6 +24,9 @@ Bug fixes
   reinstated for :class:`DataArray` and :class:`Dataset` objects only. Internal xarray
   objects remain unaddressable by weakref in order to save memory.
   (:issue:`3317`) by `Guido Imperiale <https://github.com/crusaderky>`_.
+- Line plots with the ``x`` or ``y`` argument set to a 1D non-dimensional coord
+  now plot the correct data for 2D DataArrays.
+  (:issue:`3334`). By `Tom Nicholas <http://github.com/TomNicholas>`_.
 
 Documentation
 ~~~~~~~~~~~~~
@@ -544,8 +547,9 @@ Bug fixes
   from higher frequencies to lower frequencies.  Datapoints outside the bounds
   of the original time coordinate are now filled with NaN (:issue:`2197`). By
   `Spencer Clark <https://github.com/spencerkclark>`_.
-- Line plots with the ``x`` argument set to a non-dimensional coord now plot the correct data for 1D DataArrays.
-  (:issue:`27251`). By `Tom Nicholas <http://github.com/TomNicholas>`_.
+- Line plots with the ``x`` argument set to a non-dimensional coord now plot
+  the correct data for 1D DataArrays.
+  (:issue:`2725`). By `Tom Nicholas <http://github.com/TomNicholas>`_.
 - Subtracting a scalar ``cftime.datetime`` object from a
   :py:class:`CFTimeIndex` now results in a :py:class:`pandas.TimedeltaIndex`
   instead of raising a ``TypeError`` (:issue:`2671`).  By `Spencer Clark
diff --git a/xarray/plot/plot.py b/xarray/plot/plot.py
index 8ca62ef58f1..7938f9b027b 100644
--- a/xarray/plot/plot.py
+++ b/xarray/plot/plot.py
@@ -83,7 +83,9 @@ def _infer_line_data(darray, x, y, hue):
                     )
 
             else:
-                yplt = darray.transpose(xname, huename)
+                xdim, = darray[xname].dims
+                huedim, = darray[huename].dims
+                yplt = darray.transpose(xdim, huedim)
 
         else:
             yname, huename = _infer_xy_labels(darray=darray, x=y, y=hue)
@@ -100,7 +102,9 @@ def _infer_line_data(darray, x, y, hue):
                     )
 
             else:
-                xplt = darray.transpose(yname, huename)
+                ydim, = darray[yname].dims
+                huedim, = darray[huename].dims
+                xplt = darray.transpose(ydim, huedim)
 
         huelabel = label_from_attrs(darray[huename])
         hueplt = darray[huename]
diff --git a/xarray/tests/test_plot.py b/xarray/tests/test_plot.py
index 020a49b0114..5ce75ad2396 100644
--- a/xarray/tests/test_plot.py
+++ b/xarray/tests/test_plot.py
@@ -170,6 +170,23 @@ def test_infer_line_data(self):
         line = current.plot.line()[0]
         assert_array_equal(line.get_xdata(), current.coords["t"].values)
 
+    def test_line_plot_along_1d_coord(self):
+        # Test for bug in GH #3334
+        x_coord = xr.DataArray(data=[0.1, 0.2], dims=["x"])
+        t_coord = xr.DataArray(data=[10, 20], dims=["t"])
+
+        da = xr.DataArray(
+            data=np.array([[0, 1], [5, 9]]),
+            dims=["x", "t"],
+            coords={"x": x_coord, "time": t_coord},
+        )
+
+        line = da.plot(x="time", hue="x")[0]
+        assert_array_equal(line.get_xdata(), da.coords["time"].values)
+
+        line = da.plot(y="time", hue="x")[0]
+        assert_array_equal(line.get_ydata(), da.coords["time"].values)
+
     def test_2d_line(self):
         with raises_regex(ValueError, "hue"):
             self.darray[:, :, 0].plot.line()