diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index 032bcf09244e5..1ca513e8f5e6a 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -662,6 +662,7 @@ Missing
 - Bug in :meth:`Index.equals` raising ``TypeError`` when :class:`Index` consists of tuples that contain ``NA`` (:issue:`48446`)
 - Bug in :meth:`Series.map` caused incorrect result when data has NaNs and defaultdict mapping was used (:issue:`48813`)
 - Bug in :class:`NA` raising a ``TypeError`` instead of return :class:`NA` when performing a binary operation with a ``bytes`` object (:issue:`49108`)
+- Bug in :meth:`DataFrame.update` with ``overwrite=False`` raising ``TypeError`` when ``self`` has column with ``NaT`` values and column not present in ``other`` (:issue:`16713`)
 
 MultiIndex
 ^^^^^^^^^^
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index b465761c45c78..ca763151e29a0 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -8056,11 +8056,12 @@ def update(
         if not isinstance(other, DataFrame):
             other = DataFrame(other)
 
-        other = other.reindex_like(self)
+        other = other.reindex(self.index)
 
-        for col in self.columns:
+        for col in self.columns.intersection(other.columns):
             this = self[col]._values
             that = other[col]._values
+
             if filter_func is not None:
                 with np.errstate(all="ignore"):
                     mask = ~filter_func(this) | isna(that)
diff --git a/pandas/tests/frame/methods/test_update.py b/pandas/tests/frame/methods/test_update.py
index a35530100a425..40f87f1382625 100644
--- a/pandas/tests/frame/methods/test_update.py
+++ b/pandas/tests/frame/methods/test_update.py
@@ -166,3 +166,13 @@ def test_update_modify_view(self, using_copy_on_write):
             tm.assert_frame_equal(result_view, df2_orig)
         else:
             tm.assert_frame_equal(result_view, expected)
+
+    def test_update_dt_column_with_NaT_create_column(self):
+        # GH#16713
+        df = DataFrame({"A": [1, None], "B": [pd.NaT, pd.to_datetime("2016-01-01")]})
+        df2 = DataFrame({"A": [2, 3]})
+        df.update(df2, overwrite=False)
+        expected = DataFrame(
+            {"A": [1.0, 3.0], "B": [pd.NaT, pd.to_datetime("2016-01-01")]}
+        )
+        tm.assert_frame_equal(df, expected)