diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 184cee05ae2..39ba72063ef 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -54,6 +54,8 @@ 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>`_.
 
 .. _whats-new.0.11.3:
 
diff --git a/xarray/plot/plot.py b/xarray/plot/plot.py
index 13d6ec31104..9178dd8f031 100644
--- a/xarray/plot/plot.py
+++ b/xarray/plot/plot.py
@@ -200,18 +200,22 @@ def _infer_line_data(darray, x, y, hue):
                          'for line plots.')
 
     if ndims == 1:
-        dim, = darray.dims  # get the only dimension name
         huename = None
         hueplt = None
         huelabel = ''
 
-        if (x is None and y is None) or x == dim:
-            xplt = darray[dim]
+        if x is not None:
+            xplt = darray[x]
             yplt = darray
 
-        else:
-            yplt = darray[dim]
+        elif y is not None:
             xplt = darray
+            yplt = darray[y]
+
+        else:  # Both x & y are None
+            dim = darray.dims[0]
+            xplt = darray[dim]
+            yplt = darray
 
     else:
         if x is None and y is None and hue is None:
diff --git a/xarray/tests/test_plot.py b/xarray/tests/test_plot.py
index 529d35db865..3b08ce706f5 100644
--- a/xarray/tests/test_plot.py
+++ b/xarray/tests/test_plot.py
@@ -4,6 +4,7 @@
 import numpy as np
 import pandas as pd
 import pytest
+from numpy.testing import assert_array_equal
 
 import xarray as xr
 import xarray.plot as xplt
@@ -140,6 +141,20 @@ def test_1d_x_y_kw(self):
         with raises_regex(ValueError, 'None'):
             da.plot(x='z', y='f')
 
+    # Test for bug in GH issue #2725
+    def test_infer_line_data(self):
+        current = DataArray(name='I', data=np.array([5, 8]), dims=['t'],
+                            coords={'t': (['t'], np.array([0.1, 0.2])),
+                                    'V': (['t'], np.array([100, 200]))})
+
+        # Plot current against voltage
+        line = current.plot.line(x='V')[0]
+        assert_array_equal(line.get_xdata(), current.coords['V'].values)
+
+        # Plot current against time
+        line = current.plot.line()[0]
+        assert_array_equal(line.get_xdata(), current.coords['t'].values)
+
     def test_2d_line(self):
         with raises_regex(ValueError, 'hue'):
             self.darray[:, :, 0].plot.line()