diff --git a/ci/requirements-3.7-0.24.2.conda b/ci/requirements-3.7-0.24.2.conda
index 82f4e7b9..e0323d92 100644
--- a/ci/requirements-3.7-0.24.2.conda
+++ b/ci/requirements-3.7-0.24.2.conda
@@ -1,6 +1,6 @@
 codecov
 coverage
-db-dtypes==0.3.0
+db-dtypes==0.3.1
 fastavro
 flake8
 numpy==1.16.6
diff --git a/pandas_gbq/load.py b/pandas_gbq/load.py
index 5422402e..315ad5cd 100644
--- a/pandas_gbq/load.py
+++ b/pandas_gbq/load.py
@@ -90,12 +90,13 @@ def cast_dataframe_for_parquet(
             # Use extension dtype first so that it uses the correct equality operator.
             and db_dtypes.DateDtype() != dataframe[column_name].dtype
         ):
-            # Construct converted column manually, because I can't use
-            # .astype() with DateDtype. With .astype(), I get the error:
-            #
-            # TypeError: Cannot interpret '<db_dtypes.DateDtype ...>' as a data type
-            cast_column = pandas.Series(
-                dataframe[column_name], dtype=db_dtypes.DateDtype()
+            cast_column = dataframe[column_name].astype(
+                dtype=db_dtypes.DateDtype(),
+                # Return the original column if there was an error converting
+                # to the dtype, such as is there is a date outside the
+                # supported range.
+                # https://github.com/googleapis/python-bigquery-pandas/issues/441
+                errors="ignore",
             )
         elif column_type in {"NUMERIC", "DECIMAL", "BIGNUMERIC", "BIGDECIMAL"}:
             cast_column = dataframe[column_name].map(decimal.Decimal)
diff --git a/setup.py b/setup.py
index 28c81eee..283e5ea8 100644
--- a/setup.py
+++ b/setup.py
@@ -23,16 +23,16 @@
 release_status = "Development Status :: 4 - Beta"
 dependencies = [
     "setuptools",
-    "db-dtypes >=0.3.0,<2.0.0",
-    "numpy>=1.16.6",
-    "pandas>=0.24.2",
+    "db-dtypes >=0.3.1,<2.0.0",
+    "numpy >=1.16.6",
+    "pandas >=0.24.2",
     "pyarrow >=3.0.0, <7.0dev",
     "pydata-google-auth",
     "google-auth",
     "google-auth-oauthlib",
     # 2.4.* has a bug where waiting for the query can hang indefinitely.
     # https://github.com/pydata/pandas-gbq/issues/343
-    "google-cloud-bigquery[bqstorage,pandas]>=1.11.1,<3.0.0dev,!=2.4.*",
+    "google-cloud-bigquery[bqstorage,pandas] >=1.11.1,<3.0.0dev,!=2.4.*",
 ]
 extras = {
     "tqdm": "tqdm>=4.23.0",
diff --git a/testing/constraints-3.7.txt b/testing/constraints-3.7.txt
index 7920656a..6c3080dc 100644
--- a/testing/constraints-3.7.txt
+++ b/testing/constraints-3.7.txt
@@ -5,7 +5,7 @@
 #
 # e.g., if setup.py has "foo >= 1.14.0, < 2.0.0dev",
 # Then this file should have foo==1.14.0
-db-dtypes==0.3.0
+db-dtypes==0.3.1
 google-auth==1.4.1
 google-auth-oauthlib==0.0.1
 google-cloud-bigquery==1.11.1
diff --git a/tests/system/test_to_gbq.py b/tests/system/test_to_gbq.py
index 4421f3be..f7184024 100644
--- a/tests/system/test_to_gbq.py
+++ b/tests/system/test_to_gbq.py
@@ -188,6 +188,54 @@ def test_series_round_trip(
             {"name": "num_col", "type": "NUMERIC"},
         ],
     ),
+    pytest.param(
+        *DataFrameRoundTripTestCase(
+            input_df=pandas.DataFrame(
+                {
+                    "row_num": [1, 2, 3],
+                    # DATE valuess outside the pandas range for timestamp
+                    # aren't supported by the db-dtypes package.
+                    # https://github.com/googleapis/python-bigquery-pandas/issues/441
+                    "date_col": [
+                        datetime.date(1, 1, 1),
+                        datetime.date(1970, 1, 1),
+                        datetime.date(9999, 12, 31),
+                    ],
+                    # TODO: DATETIME/TIMESTAMP values outside of the range for
+                    # pandas timestamp require `date_as_object` parameter in
+                    # google-cloud-bigquery versions 1.x and 2.x.
+                    # https://github.com/googleapis/python-bigquery-pandas/issues/365
+                    # "datetime_col": [
+                    #     datetime.datetime(1, 1, 1),
+                    #     datetime.datetime(1970, 1, 1),
+                    #     datetime.datetime(9999, 12, 31, 23, 59, 59, 999999),
+                    # ],
+                    # "timestamp_col": [
+                    #     datetime.datetime(1, 1, 1, tzinfo=datetime.timezone.utc),
+                    #     datetime.datetime(1970, 1, 1, tzinfo=datetime.timezone.utc),
+                    #     datetime.datetime(
+                    #         9999,
+                    #         12,
+                    #         31,
+                    #         23,
+                    #         59,
+                    #         59,
+                    #         999999,
+                    #         tzinfo=datetime.timezone.utc,
+                    #     ),
+                    # ],
+                },
+                columns=["row_num", "date_col", "datetime_col", "timestamp_col"],
+            ),
+            table_schema=[
+                {"name": "row_num", "type": "INTEGER"},
+                {"name": "date_col", "type": "DATE"},
+                {"name": "datetime_col", "type": "DATETIME"},
+                {"name": "timestamp_col", "type": "TIMESTAMP"},
+            ],
+        ),
+        id="issue365-extreme-datetimes",
+    ),
 ]