diff --git a/rest_framework/pagination.py b/rest_framework/pagination.py
index dc120d8e8..75b06f1e8 100644
--- a/rest_framework/pagination.py
+++ b/rest_framework/pagination.py
@@ -2,15 +2,20 @@
 Pagination serializers determine the structure of the output that should
 be used for paginated responses.
 """
+import json
+import operator
+
 from base64 import b64decode, b64encode
 from collections import OrderedDict, namedtuple
 from urllib import parse
+from functools import reduce
 
 from django.core.paginator import InvalidPage
 from django.core.paginator import Paginator as DjangoPaginator
 from django.template import loader
 from django.utils.encoding import force_str
 from django.utils.translation import gettext_lazy as _
+from django.db.models.query import Q
 
 from rest_framework.compat import coreapi, coreschema
 from rest_framework.exceptions import NotFound
@@ -616,25 +621,41 @@ class CursorPagination(BasePagination):
         else:
             (offset, reverse, current_position) = self.cursor
 
-        # Cursor pagination always enforces an ordering.
-        if reverse:
-            queryset = queryset.order_by(*_reverse_ordering(self.ordering))
-        else:
-            queryset = queryset.order_by(*self.ordering)
-
         # If we have a cursor with a fixed position then filter by that.
         if current_position is not None:
-            order = self.ordering[0]
-            is_reversed = order.startswith('-')
-            order_attr = order.lstrip('-')
+            current_position_list = json.loads(current_position)
 
-            # Test for: (cursor reversed) XOR (queryset reversed)
-            if self.cursor.reverse != is_reversed:
-                kwargs = {order_attr + '__lt': current_position}
-            else:
-                kwargs = {order_attr + '__gt': current_position}
+            q_objects_equals = {}
+            q_objects_compare = {}
 
-            queryset = queryset.filter(**kwargs)
+            for order, position in zip(self.ordering, current_position_list):
+                is_reversed = order.startswith("-")
+                order_attr = order.lstrip("-")
+
+                q_objects_equals[order] = Q(**{order_attr: position})
+
+                # Test for: (cursor reversed) XOR (queryset reversed)
+                if self.cursor.reverse != is_reversed:
+                    q_objects_compare[order] = Q(
+                        **{(order_attr + "__lt"): position}
+                    )
+                else:
+                    q_objects_compare[order] = Q(
+                        **{(order_attr + "__gt"): position}
+                    )
+
+            filter_list = []
+            # starting with the second field
+            for i in range(len(self.ordering)):
+                # The first operands need to be equals
+                # the last operands need to be gt
+                equals = list(self.ordering[:i+2])
+                greater_than_q = q_objects_compare[equals.pop()]
+                sub_filters = [q_objects_equals[e] for e in equals]
+                sub_filters.append(greater_than_q)
+                filter_list.append(reduce(operator.and_, sub_filters))
+
+            queryset = queryset.filter(reduce(operator.or_, filter_list))
 
         # If we have an offset cursor then offset the entire page by that amount.
         # We also always fetch an extra item in order to determine if there is a
@@ -839,7 +860,14 @@ class CursorPagination(BasePagination):
         )
 
         if isinstance(ordering, str):
-            return (ordering,)
+            ordering = (ordering,)
+
+        pk_name = queryset.model._meta.pk.name
+
+        # Always include a unique key to order by
+        if not {f"-{pk_name}", pk_name, "pk", "-pk"} & set(ordering):
+            ordering = ordering + (pk_name,)
+
         return tuple(ordering)
 
     def decode_cursor(self, request):
@@ -884,12 +912,18 @@ class CursorPagination(BasePagination):
         return replace_query_param(self.base_url, self.cursor_query_param, encoded)
 
     def _get_position_from_instance(self, instance, ordering):
-        field_name = ordering[0].lstrip('-')
-        if isinstance(instance, dict):
-            attr = instance[field_name]
-        else:
-            attr = getattr(instance, field_name)
-        return str(attr)
+        fields = []
+
+        for o in ordering:
+            field_name = o.lstrip("-")
+            if isinstance(instance, dict):
+                attr = instance[field_name]
+            else:
+                attr = getattr(instance, field_name)
+
+            fields.append(str(attr))
+
+        return json.dumps(fields).encode()
 
     def get_paginated_response(self, data):
         return Response(OrderedDict([