diff --git a/dvc/fs/base.py b/dvc/fs/base.py
index b710fdcfb..c54bfc14b 100644
--- a/dvc/fs/base.py
+++ b/dvc/fs/base.py
@@ -331,7 +331,7 @@ class BaseFileSystem:
             return None
 
         to_infos = (
-            localfs.path.join(to_info, self.path.relpath(info, from_info))
+            localfs.path.join(to_info, *self.path.relparts(info, from_info))
             for info in from_infos
         )
         callback.set_size(len(from_infos))
diff --git a/dvc/fs/path.py b/dvc/fs/path.py
index 584ec9b73..f06c3b122 100644
--- a/dvc/fs/path.py
+++ b/dvc/fs/path.py
@@ -77,5 +77,8 @@ class Path:
         normbase = base.rstrip(self.sep)
         return normpath[len(normbase) + 1 :]
 
+    def relparts(self, path, base):
+        return self.parts(self.relpath(path, base))
+
     def as_posix(self, path):
         return path.replace(self.sep, posixpath.sep)
diff --git a/dvc/objects/stage.py b/dvc/objects/stage.py
index b3a88e443..f298cef6e 100644
--- a/dvc/objects/stage.py
+++ b/dvc/objects/stage.py
@@ -163,8 +163,7 @@ def _build_tree(fs_path, fs, name, **kwargs):
         # Yes, this is a BUG, as long as we permit "/" in
         # filenames on Windows and "\" on Unix
 
-        relpath = fs.path.relpath(file_fs_path, fs_path)
-        key = tuple(relpath.split(fs.path.sep))
+        key = fs.path.relparts(file_fs_path, fs_path)
         assert key
         tree.add(key, meta, obj.hash_info)
 
diff --git a/dvc/output.py b/dvc/output.py
index 6a798e0e3..4abb1c8c4 100644
--- a/dvc/output.py
+++ b/dvc/output.py
@@ -718,7 +718,7 @@ class Output:
 
         fs_path = self.fs.path
         if filter_info and filter_info != self.fs_path:
-            prefix = fs_path.parts(fs_path.relpath(filter_info, self.fs_path))
+            prefix = fs_path.relparts(filter_info, self.fs_path)
             obj = obj.get(self.odb, prefix)
 
         return obj