diff --git a/CHANGES.rst b/CHANGES.rst
index fa24b104..55caae37 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -23,7 +23,9 @@ Unreleased
 -   Roll back a change to the order that URL matching was done. The
     URL is again matched after the session is loaded, so the session is
     available in custom URL converters. :issue:`4053`
-
+-   Fix the request ``blueprint`` method to ensure it returns the
+    current blueprint name. A ``blueprints`` method is added to
+    replace any functionality lost in this fix. :pr:`4059`
 
 Version 2.0.0
 -------------
diff --git a/src/flask/app.py b/src/flask/app.py
index f0f31486..38bd303b 100644
--- a/src/flask/app.py
+++ b/src/flask/app.py
@@ -747,7 +747,7 @@ class Flask(Scaffold):
         ] = self.template_context_processors[None]
         reqctx = _request_ctx_stack.top
         if reqctx is not None:
-            for bp in self._request_blueprints():
+            for bp in request.blueprints:
                 if bp in self.template_context_processors:
                     funcs = chain(funcs, self.template_context_processors[bp])
         orig_ctx = context.copy()
@@ -1261,7 +1261,7 @@ class Flask(Scaffold):
         exc_class, code = self._get_exc_class_and_code(type(e))
 
         for c in [code, None]:
-            for name in chain(self._request_blueprints(), [None]):
+            for name in chain(request.blueprints, [None]):
                 handler_map = self.error_handler_spec[name][c]
 
                 if not handler_map:
@@ -1825,14 +1825,14 @@ class Flask(Scaffold):
         funcs: t.Iterable[URLValuePreprocessorCallable] = self.url_value_preprocessors[
             None
         ]
-        for bp in self._request_blueprints():
+        for bp in request.blueprints:
             if bp in self.url_value_preprocessors:
                 funcs = chain(funcs, self.url_value_preprocessors[bp])
         for func in funcs:
             func(request.endpoint, request.view_args)
 
         funcs: t.Iterable[BeforeRequestCallable] = self.before_request_funcs[None]
-        for bp in self._request_blueprints():
+        for bp in request.blueprints:
             if bp in self.before_request_funcs:
                 funcs = chain(funcs, self.before_request_funcs[bp])
         for func in funcs:
@@ -1857,7 +1857,7 @@ class Flask(Scaffold):
         """
         ctx = _request_ctx_stack.top
         funcs: t.Iterable[AfterRequestCallable] = ctx._after_request_functions
-        for bp in self._request_blueprints():
+        for bp in request.blueprints:
             if bp in self.after_request_funcs:
                 funcs = chain(funcs, reversed(self.after_request_funcs[bp]))
         if None in self.after_request_funcs:
@@ -1896,7 +1896,7 @@ class Flask(Scaffold):
         funcs: t.Iterable[TeardownCallable] = reversed(
             self.teardown_request_funcs[None]
         )
-        for bp in self._request_blueprints():
+        for bp in request.blueprints:
             if bp in self.teardown_request_funcs:
                 funcs = chain(funcs, reversed(self.teardown_request_funcs[bp]))
         for func in funcs:
@@ -2068,9 +2068,3 @@ class Flask(Scaffold):
         wrapped to apply middleware.
         """
         return self.wsgi_app(environ, start_response)
-
-    def _request_blueprints(self) -> t.Iterable[str]:
-        if _request_ctx_stack.top.request.blueprint is None:
-            return []
-        else:
-            return reversed(_request_ctx_stack.top.request.blueprint.split("."))
diff --git a/src/flask/wrappers.py b/src/flask/wrappers.py
index bfa9d7ce..4f118213 100644
--- a/src/flask/wrappers.py
+++ b/src/flask/wrappers.py
@@ -1,6 +1,7 @@
 import typing as t
 
 from werkzeug.exceptions import BadRequest
+from werkzeug.utils import cached_property
 from werkzeug.wrappers import Request as RequestBase
 from werkzeug.wrappers import Response as ResponseBase
 
@@ -73,10 +74,24 @@ class Request(RequestBase):
     def blueprint(self) -> t.Optional[str]:
         """The name of the current blueprint"""
         if self.url_rule and "." in self.url_rule.endpoint:
-            return self.url_rule.endpoint.rsplit(".", 1)[0]
+            return self.url_rule.endpoint.split(".")[-2]
         else:
             return None
 
+    @cached_property
+    def blueprints(self) -> t.List[str]:
+        """Return the names of the current blueprints.
+
+        The returned list is ordered from the current blueprint,
+        upwards through parent blueprints.
+        """
+        if self.url_rule and "." in self.url_rule.endpoint:
+            bps = self.url_rule.endpoint.split(".")[:-1]
+            bps.reverse()
+            return bps
+        else:
+            return []
+
     def _load_form_data(self) -> None:
         RequestBase._load_form_data(self)