diff --git a/django/db/backends/base/features.py b/django/db/backends/base/features.py
index 70878f92a2..0009de7a60 100644
--- a/django/db/backends/base/features.py
+++ b/django/db/backends/base/features.py
@@ -288,6 +288,9 @@ class BaseDatabaseFeatures:
     # field(s)?
     allows_multiple_constraints_on_same_fields = True
 
+    # Does the backend support boolean expressions in the SELECT clause?
+    supports_boolean_expr_in_select_clause = True
+
     def __init__(self, connection):
         self.connection = connection
 
diff --git a/django/db/backends/oracle/features.py b/django/db/backends/oracle/features.py
index 2da11355ed..73a6e86686 100644
--- a/django/db/backends/oracle/features.py
+++ b/django/db/backends/oracle/features.py
@@ -58,3 +58,4 @@ class DatabaseFeatures(BaseDatabaseFeatures):
     supports_partial_indexes = False
     supports_slicing_ordering_in_compound = True
     allows_multiple_constraints_on_same_fields = False
+    supports_boolean_expr_in_select_clause = False
diff --git a/django/db/models/expressions.py b/django/db/models/expressions.py
index 16924be9f6..5f85b47423 100644
--- a/django/db/models/expressions.py
+++ b/django/db/models/expressions.py
@@ -1075,12 +1075,11 @@ class Exists(Subquery):
             sql = 'NOT {}'.format(sql)
         return sql, params
 
-    def as_oracle(self, compiler, connection, template=None, **extra_context):
-        # Oracle doesn't allow EXISTS() in the SELECT list, so wrap it with a
-        # CASE WHEN expression. Change the template since the When expression
-        # requires a left hand side (column) to compare against.
-        sql, params = self.as_sql(compiler, connection, template, **extra_context)
-        sql = 'CASE WHEN {} THEN 1 ELSE 0 END'.format(sql)
+    def select_format(self, compiler, sql, params):
+        # Wrap EXISTS() with a CASE WHEN expression if a database backend
+        # (e.g. Oracle) doesn't support boolean expression in the SELECT list.
+        if not compiler.connection.features.supports_boolean_expr_in_select_clause:
+            sql = 'CASE WHEN {} THEN 1 ELSE 0 END'.format(sql)
         return sql, params
 
 
@@ -1140,6 +1139,19 @@ class OrderBy(BaseExpression):
             template = 'IF(ISNULL(%(expression)s),0,1), %(expression)s %(ordering)s '
         return self.as_sql(compiler, connection, template=template)
 
+    def as_oracle(self, compiler, connection):
+        # Oracle doesn't allow ORDER BY EXISTS() unless it's wrapped in
+        # a CASE WHEN.
+        if isinstance(self.expression, Exists):
+            copy = self.copy()
+            # XXX: Use Case(When(self.lhs)) once support for boolean
+            # expressions is added to When.
+            exists_sql, params = compiler.compile(self.expression)
+            case_sql = 'CASE WHEN %s THEN 1 ELSE 0 END' % exists_sql
+            copy.expression = RawSQL(case_sql, params)
+            return copy.as_sql(compiler, connection)
+        return self.as_sql(compiler, connection)
+
     def get_group_by_cols(self, alias=None):
         cols = []
         for source in self.get_source_expressions():
diff --git a/django/db/models/lookups.py b/django/db/models/lookups.py
index 186e217083..f76c1e391b 100644
--- a/django/db/models/lookups.py
+++ b/django/db/models/lookups.py
@@ -3,7 +3,7 @@ import math
 from copy import copy
 
 from django.core.exceptions import EmptyResultSet
-from django.db.models.expressions import Func, Value
+from django.db.models.expressions import Exists, Func, RawSQL, Value
 from django.db.models.fields import DateTimeField, Field, IntegerField
 from django.db.models.query_utils import RegisterLookupMixin
 from django.utils.datastructures import OrderedSet
@@ -112,6 +112,23 @@ class Lookup:
     def as_sql(self, compiler, connection):
         raise NotImplementedError
 
+    def as_oracle(self, compiler, connection):
+        # Oracle doesn't allow EXISTS() to be compared to another expression
+        # unless it's wrapped in a CASE WHEN.
+        wrapped = False
+        exprs = []
+        for expr in (self.lhs, self.rhs):
+            if isinstance(expr, Exists):
+                # XXX: Use Case(When(self.lhs)) once support for boolean
+                # expressions is added to When.
+                sql, params = compiler.compile(expr)
+                sql = 'CASE WHEN %s THEN 1 ELSE 0 END' % sql
+                expr = RawSQL(sql, params)
+                wrapped = True
+            exprs.append(expr)
+        lookup = type(self)(*exprs) if wrapped else self
+        return lookup.as_sql(compiler, connection)
+
     @cached_property
     def contains_aggregate(self):
         return self.lhs.contains_aggregate or getattr(self.rhs, 'contains_aggregate', False)