diff --git a/CHANGES b/CHANGES
index b83f1925f..3f2fbbf7e 100644
--- a/CHANGES
+++ b/CHANGES
@@ -200,6 +200,7 @@ Bugs fixed
 * #5114: sphinx-build: Handle errors on scanning documents
 * epub: spine has been broken when "self" is listed on toctree (refs: #4611)
 * #344: autosummary does not understand docstring of module level attributes
+* #5002: graphviz: SVGs do not adapt to the column width
 
 Testing
 --------
diff --git a/sphinx/ext/graphviz.py b/sphinx/ext/graphviz.py
index 11d9e54a0..3b33c7b79 100644
--- a/sphinx/ext/graphviz.py
+++ b/sphinx/ext/graphviz.py
@@ -27,6 +27,7 @@ from sphinx.errors import SphinxError
 from sphinx.locale import _, __
 from sphinx.util import logging
 from sphinx.util.docutils import SphinxDirective
+from sphinx.util.fileutil import copy_asset_file
 from sphinx.util.i18n import search_image_for_language
 from sphinx.util.osutil import ensuredir, ENOENT, EPIPE, EINVAL
 
@@ -281,19 +282,23 @@ def render_dot_html(self, node, code, options, prefix='graphviz',
         logger.warning(__('dot code %r: %s'), code, text_type(exc))
         raise nodes.SkipNode
 
+    if imgcls:
+        imgcls += " graphviz"
+    else:
+        imgcls = "graphviz"
+
     if fname is None:
         self.body.append(self.encode(code))
     else:
         if alt is None:
             alt = node.get('alt', self.encode(code).strip())
-        imgcss = imgcls and 'class="%s"' % imgcls or ''
         if 'align' in node:
             self.body.append('<div align="%s" class="align-%s">' %
                              (node['align'], node['align']))
         if format == 'svg':
             self.body.append('<div class="graphviz">')
-            self.body.append('<object data="%s" type="image/svg+xml" %s>\n' %
-                             (fname, imgcss))
+            self.body.append('<object data="%s" type="image/svg+xml" class="%s">\n' %
+                             (fname, imgcls))
             self.body.append('<p class="warning">%s</p>' % alt)
             self.body.append('</object></div>\n')
         else:
@@ -302,15 +307,15 @@ def render_dot_html(self, node, code, options, prefix='graphviz',
                 if imgmap.clickable:
                     # has a map
                     self.body.append('<div class="graphviz">')
-                    self.body.append('<img src="%s" alt="%s" usemap="#%s" %s/>' %
-                                     (fname, alt, imgmap.id, imgcss))
+                    self.body.append('<img src="%s" alt="%s" usemap="#%s" class="%s" />' %
+                                     (fname, alt, imgmap.id, imgcls))
                     self.body.append('</div>\n')
                     self.body.append(imgmap.generate_clickable_map())
                 else:
                     # nothing in image map
                     self.body.append('<div class="graphviz">')
-                    self.body.append('<img src="%s" alt="%s" %s/>' %
-                                     (fname, alt, imgcss))
+                    self.body.append('<img src="%s" alt="%s" class="%s" />' %
+                                     (fname, alt, imgcls))
                     self.body.append('</div>\n')
         if 'align' in node:
             self.body.append('</div>\n')
@@ -396,6 +401,14 @@ def man_visit_graphviz(self, node):
     raise nodes.SkipNode
 
 
+def on_build_finished(app, exc):
+    # type: (Sphinx, Exception) -> None
+    if exc is None:
+        src = path.join(sphinx.package_dir, 'templates', 'graphviz', 'graphviz.css')
+        dst = path.join(app.outdir, '_static')
+        copy_asset_file(src, dst)
+
+
 def setup(app):
     # type: (Sphinx) -> Dict[unicode, Any]
     app.add_node(graphviz,
@@ -410,4 +423,6 @@ def setup(app):
     app.add_config_value('graphviz_dot', 'dot', 'html')
     app.add_config_value('graphviz_dot_args', [], 'html')
     app.add_config_value('graphviz_output_format', 'png', 'html')
+    app.add_css_file('graphviz.css')
+    app.connect('build-finished', on_build_finished)
     return {'version': sphinx.__display_version__, 'parallel_read_safe': True}
diff --git a/sphinx/templates/graphviz/graphviz.css b/sphinx/templates/graphviz/graphviz.css
new file mode 100644
index 000000000..1f246c8d9
--- /dev/null
+++ b/sphinx/templates/graphviz/graphviz.css
@@ -0,0 +1,19 @@
+/*
+ * graphviz.css
+ * ~~~~~~~~~~~~
+ *
+ * Sphinx stylesheet -- graphviz extension.
+ *
+ * :copyright: Copyright 2007-2018 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+
+img.graphviz {
+    border: 0;
+    max-width: 100%;
+}
+
+object.graphviz {
+    max-width: 100%;
+}
diff --git a/tests/test_ext_graphviz.py b/tests/test_ext_graphviz.py
index 9b53876db..d0358b407 100644
--- a/tests/test_ext_graphviz.py
+++ b/tests/test_ext_graphviz.py
@@ -30,7 +30,7 @@ def test_graphviz_png_html(app, status, warning):
     html = 'Hello <div class="graphviz"><img .*?/></div>\n graphviz world'
     assert re.search(html, content, re.S)
 
-    html = '<img src=".*?" alt="digraph {\n  bar -&gt; baz\n}" />'
+    html = '<img src=".*?" alt="digraph {\n  bar -&gt; baz\n}" class="graphviz" />'
     assert re.search(html, content, re.M)
 
     html = (r'<div class="figure align-right" .*?>\s*'
@@ -41,7 +41,7 @@ def test_graphviz_png_html(app, status, warning):
     html = (r'<div align=\"center\" class=\"align-center\">'
             r'<div class="graphviz"><img src=\".*\.png\" alt=\"digraph foo {\n'
             r'centered\n'
-            r'}\" /></div>\n</div>')
+            r'}\" class="graphviz" /></div>\n</div>')
     assert re.search(html, content, re.S)
 
 
@@ -117,7 +117,7 @@ def test_graphviz_i18n(app, status, warning):
     app.builder.build_all()
 
     content = (app.outdir / 'index.html').text()
-    html = '<img src=".*?" alt="digraph {\n  BAR -&gt; BAZ\n}" />'
+    html = '<img src=".*?" alt="digraph {\n  BAR -&gt; BAZ\n}" class="graphviz" />'
     assert re.search(html, content, re.M)
 
 
diff --git a/tests/test_ext_inheritance_diagram.py b/tests/test_ext_inheritance_diagram.py
index 8456cda4a..711e0712c 100644
--- a/tests/test_ext_inheritance_diagram.py
+++ b/tests/test_ext_inheritance_diagram.py
@@ -27,8 +27,8 @@ def test_inheritance_diagram_png_html(app, status, warning):
     pattern = ('<div class="figure" id="id1">\n'
                '<div class="graphviz">'
                '<img src="_images/inheritance-\\w+.png" alt="Inheritance diagram of test.Foo" '
-               'class="inheritance"/></div>\n<p class="caption"><span class="caption-text">'
-               'Test Foo!</span><a class="headerlink" href="#id1" '
+               'class="inheritance graphviz" /></div>\n<p class="caption">'
+               '<span class="caption-text">Test Foo!</span><a class="headerlink" href="#id1" '
                'title="Permalink to this image">\xb6</a></p>')
     assert re.search(pattern, content, re.M)
 
@@ -44,7 +44,7 @@ def test_inheritance_diagram_svg_html(app, status, warning):
     pattern = ('<div class="figure" id="id1">\n'
                '<div class="graphviz">'
                '<object data="_images/inheritance-\\w+.svg" '
-               'type="image/svg\\+xml" class="inheritance">\n'
+               'type="image/svg\\+xml" class="inheritance graphviz">\n'
                '<p class=\"warning\">Inheritance diagram of test.Foo</p>'
                '</object></div>\n<p class="caption"><span class="caption-text">'
                'Test Foo!</span><a class="headerlink" href="#id1" '
@@ -84,8 +84,8 @@ def test_inheritance_diagram_latex_alias(app, status, warning):
     pattern = ('<div class="figure" id="id1">\n'
                '<div class="graphviz">'
                '<img src="_images/inheritance-\\w+.png" alt="Inheritance diagram of test.Foo" '
-               'class="inheritance"/></div>\n<p class="caption"><span class="caption-text">'
-               'Test Foo!</span><a class="headerlink" href="#id1" '
+               'class="inheritance graphviz" /></div>\n<p class="caption">'
+               '<span class="caption-text">Test Foo!</span><a class="headerlink" href="#id1" '
                'title="Permalink to this image">\xb6</a></p>')
     assert re.search(pattern, content, re.M)