diff --git a/CHANGES b/CHANGES
index cc3047f48..d537cd232 100644
--- a/CHANGES
+++ b/CHANGES
@@ -12,6 +12,9 @@ Dependencies
 Incompatible changes
 --------------------
 
+* #5156: the :py:mod:`sphinx.ext.graphviz: extension runs `dot` in the
+  directory of the document being built instead of in the root directory of
+  the documentation.
 * #4460: extensions which stores any data to environment should return the
   version of its env data structure as metadata.  In detail, please see
   :ref:`ext-metadata`.
diff --git a/sphinx/ext/graphviz.py b/sphinx/ext/graphviz.py
index 11d9e54a0..3c8b3ac50 100644
--- a/sphinx/ext/graphviz.py
+++ b/sphinx/ext/graphviz.py
@@ -155,7 +155,10 @@ class Graphviz(SphinxDirective):
                     line=self.lineno)]
         node = graphviz()
         node['code'] = dotcode
-        node['options'] = {}
+        node['options'] = {
+            'docname': path.splitext(self.state.document.current_source)[0],
+        }
+
         if 'graphviz_dot' in self.options:
             node['options']['graphviz_dot'] = self.options['graphviz_dot']
         if 'alt' in self.options:
@@ -192,7 +195,9 @@ class GraphvizSimple(SphinxDirective):
         node = graphviz()
         node['code'] = '%s %s {\n%s\n}\n' % \
                        (self.name, self.arguments[0], '\n'.join(self.content))
-        node['options'] = {}
+        node['options'] = {
+            'docname': path.splitext(self.state.document.current_source)[0],
+        }
         if 'graphviz_dot' in self.options:
             node['options']['graphviz_dot'] = self.options['graphviz_dot']
         if 'alt' in self.options:
@@ -235,10 +240,14 @@ def render_dot(self, code, options, format, prefix='graphviz'):
     dot_args = [graphviz_dot]
     dot_args.extend(self.builder.config.graphviz_dot_args)
     dot_args.extend(['-T' + format, '-o' + outfn])
+
+    docname = options.get('docname', 'index')
+    cwd = path.dirname(path.join(self.builder.srcdir, docname))
+
     if format == 'png':
         dot_args.extend(['-Tcmapx', '-o%s.map' % outfn])
     try:
-        p = Popen(dot_args, stdout=PIPE, stdin=PIPE, stderr=PIPE)
+        p = Popen(dot_args, stdout=PIPE, stdin=PIPE, stderr=PIPE, cwd=cwd)
     except OSError as err:
         if err.errno != ENOENT:   # No such file or directory
             raise