diff --git a/django/contrib/postgres/fields/ranges.py b/django/contrib/postgres/fields/ranges.py
index 41acc8dcb2..0bb914d383 100644
--- a/django/contrib/postgres/fields/ranges.py
+++ b/django/contrib/postgres/fields/ranges.py
@@ -1,3 +1,4 @@
+import datetime
 import json
 
 from psycopg2.extras import DateRange, DateTimeTZRange, NumericRange, Range
@@ -131,6 +132,37 @@ RangeField.register_lookup(lookups.ContainedBy)
 RangeField.register_lookup(lookups.Overlap)
 
 
+class DateTimeRangeContains(models.Lookup):
+    """
+    Lookup for Date/DateTimeRange containment to cast the rhs to the correct
+    type.
+    """
+    lookup_name = 'contains'
+
+    def process_rhs(self, compiler, connection):
+        # Transform rhs value for db lookup.
+        if isinstance(self.rhs, datetime.date):
+            output_field = models.DateTimeField() if isinstance(self.rhs, datetime.datetime) else models.DateField()
+            value = models.Value(self.rhs, output_field=output_field)
+            self.rhs = value.resolve_expression(compiler.query)
+        return super().process_rhs(compiler, connection)
+
+    def as_sql(self, compiler, connection):
+        lhs, lhs_params = self.process_lhs(compiler, connection)
+        rhs, rhs_params = self.process_rhs(compiler, connection)
+        params = lhs_params + rhs_params
+        # Cast the rhs if needed.
+        cast_sql = ''
+        if isinstance(self.rhs, models.Expression) and self.rhs._output_field_or_none:
+            cast_internal_type = self.lhs.output_field.base_field.get_internal_type()
+            cast_sql = '::{}'.format(connection.data_types.get(cast_internal_type))
+        return '%s @> %s%s' % (lhs, rhs, cast_sql), params
+
+
+DateRangeField.register_lookup(DateTimeRangeContains)
+DateTimeRangeField.register_lookup(DateTimeRangeContains)
+
+
 class RangeContainedBy(models.Lookup):
     lookup_name = 'contained_by'
     type_mapping = {
diff --git a/tests/postgres_tests/test_ranges.py b/tests/postgres_tests/test_ranges.py
index 3dd60dea0d..d87ad36438 100644
--- a/tests/postgres_tests/test_ranges.py
+++ b/tests/postgres_tests/test_ranges.py
@@ -3,7 +3,7 @@ import json
 
 from django import forms
 from django.core import exceptions, serializers
-from django.db.models import F
+from django.db.models import DateField, DateTimeField, F, Func, Value
 from django.test import override_settings
 from django.utils import timezone
 
@@ -87,6 +87,80 @@ class TestSaveLoad(PostgreSQLTestCase):
         self.assertEqual(field.base_field.model, RangesModel)
 
 
+class TestRangeContainsLookup(PostgreSQLTestCase):
+
+    @classmethod
+    def setUpTestData(cls):
+        cls.timestamps = [
+            datetime.datetime(year=2016, month=1, day=1),
+            datetime.datetime(year=2016, month=1, day=2, hour=1),
+            datetime.datetime(year=2016, month=1, day=2, hour=12),
+            datetime.datetime(year=2016, month=1, day=3),
+            datetime.datetime(year=2016, month=1, day=3, hour=1),
+            datetime.datetime(year=2016, month=2, day=2),
+        ]
+        cls.aware_timestamps = [
+            timezone.make_aware(timestamp, timezone.get_current_timezone())
+            for timestamp in cls.timestamps
+        ]
+        cls.dates = [
+            datetime.date(year=2016, month=1, day=1),
+            datetime.date(year=2016, month=1, day=2),
+            datetime.date(year=2016, month=1, day=3),
+            datetime.date(year=2016, month=1, day=4),
+            datetime.date(year=2016, month=2, day=2),
+            datetime.date(year=2016, month=2, day=3),
+        ]
+        cls.obj = RangesModel.objects.create(
+            dates=(cls.dates[0], cls.dates[3]),
+            timestamps=(cls.timestamps[0], cls.timestamps[3]),
+        )
+        cls.aware_obj = RangesModel.objects.create(
+            dates=(cls.dates[0], cls.dates[3]),
+            timestamps=(cls.aware_timestamps[0], cls.aware_timestamps[3]),
+        )
+        # Objects that don't match any queries.
+        for i in range(3, 4):
+            RangesModel.objects.create(
+                dates=(cls.dates[i], cls.dates[i + 1]),
+                timestamps=(cls.timestamps[i], cls.timestamps[i + 1]),
+            )
+            RangesModel.objects.create(
+                dates=(cls.dates[i], cls.dates[i + 1]),
+                timestamps=(cls.aware_timestamps[i], cls.aware_timestamps[i + 1]),
+            )
+
+    def test_datetime_range_contains(self):
+        filter_args = (
+            self.timestamps[1],
+            self.aware_timestamps[1],
+            (self.timestamps[1], self.timestamps[2]),
+            (self.aware_timestamps[1], self.aware_timestamps[2]),
+            Value(self.dates[0], output_field=DateTimeField()),
+            Func(F('dates'), function='lower', output_field=DateTimeField()),
+        )
+        for filter_arg in filter_args:
+            with self.subTest(filter_arg=filter_arg):
+                self.assertCountEqual(
+                    RangesModel.objects.filter(**{'timestamps__contains': filter_arg}),
+                    [self.obj, self.aware_obj],
+                )
+
+    def test_date_range_contains(self):
+        filter_args = (
+            self.timestamps[1],
+            (self.dates[1], self.dates[2]),
+            Value(self.dates[0], output_field=DateField()),
+            Func(F('timestamps'), function='lower', output_field=DateField()),
+        )
+        for filter_arg in filter_args:
+            with self.subTest(filter_arg=filter_arg):
+                self.assertCountEqual(
+                    RangesModel.objects.filter(**{'dates__contains': filter_arg}),
+                    [self.obj, self.aware_obj],
+                )
+
+
 class TestQuerying(PostgreSQLTestCase):
 
     @classmethod