diff --git a/doc/users/next_whats_new/sphinx_plot_preserve.rst b/doc/users/next_whats_new/sphinx_plot_preserve.rst
@@ -0,0 +1,32 @@
+Caching sphinx directive figure outputs
+---------------------------------------
+
+The new ``:outname:`` property for the Sphinx plot directive can
+be used to cache generated images. It is used like:
+
+.. code-block:: rst
+
+    .. plot::
+       :outname: stinkbug_plot
+
+       import matplotlib.pyplot as plt
+       import matplotlib.image as mpimg
+       import numpy as np
+       img = mpimg.imread('_static/stinkbug.png')
+       imgplot = plt.imshow(img)
+
+Without ``:outname:``, the figure generated above would normally be called,
+e.g. :file:`docfile3-4-01.png` or something equally mysterious. With
+``:outname:`` the figure generated will instead be named
+:file:`stinkbug_plot-01.png` or even :file:`stinkbug_plot.png`. This makes it
+easy to understand which output image is which and, more importantly, uniquely
+keys output images to the code snippets that generated them.
+
+Configuring the cache directory
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+The directory that images are cached to can be configured using the
+``plot_cache_dir`` configuration value in the Sphinx configuration file.
+
+If an image is already in ``plot_cache_dir`` when documentation is being
+generated, this image is copied to the build directory thereby pre-empting
+generation and reducing computation time in low-resource environments.
diff --git a/lib/matplotlib/sphinxext/plot_directive.py b/lib/matplotlib/sphinxext/plot_directive.py
@@ -77,6 +77,11 @@
         If specified, the option's argument will be used as a caption for the
         figure. This overwrites the caption given in the content, when the plot
         is generated from a file.
+    ``:outname:`` : str
+        If specified, the names of the generated plots will start with the
+        value of ``:outname:``. This is handy for preserving output results if
+        code is reordered between runs. The value of ``:outname:`` must be
+        unique across the generated documentation.
 
 Additionally, this directive supports all the options of the `image directive
 <https://docutils.sourceforge.io/docs/ref/rst/directives.html#image>`_,
@@ -139,19 +144,27 @@
 
     plot_template
         Provide a customized template for preparing restructured text.
+
+    plot_cache_dir
+        Files with outnames are copied to this directory and files in this
+        directory are copied back into the build directory prior to the build
+        beginning.
+
 """
 
 import contextlib
 import doctest
 from io import StringIO
 import itertools
 import os
-from os.path import relpath
-from pathlib import Path
-import re
-import shutil
 import sys
+import shutil
+import re
 import textwrap
+import glob
+import logging
+from os.path import relpath
+from pathlib import Path
 import traceback
 
 from docutils.parsers.rst import directives, Directive
@@ -167,6 +180,12 @@
 
 __version__ = 2
 
+_log = logging.getLogger(__name__)
+
+# Outnames must be unique. This variable stores the outnames that
+# have been seen so we can guarantee this and warn the user if a
+# duplicate is encountered.
+_outname_list = set()
 
 # -----------------------------------------------------------------------------
 # Registration hook
@@ -245,6 +264,7 @@ class PlotDirective(Directive):
         'context': _option_context,
         'nofigs': directives.flag,
         'caption': directives.unchanged,
+        'outname': str
         }
 
     def run(self):
@@ -280,6 +300,7 @@ def setup(app):
     app.add_config_value('plot_apply_rcparams', False, True)
     app.add_config_value('plot_working_directory', None, True)
     app.add_config_value('plot_template', None, True)
+    app.add_config_value('plot_cache_dir',  '', True)
     app.connect('doctree-read', mark_plot_labels)
     app.add_css_file('plot_directive.css')
     app.connect('build-finished', _copy_css_file)
@@ -517,7 +538,8 @@ def get_plot_formats(config):
 def render_figures(code, code_path, output_dir, output_base, context,
                    function_name, config, context_reset=False,
                    close_figs=False,
-                   code_includes=None):
+                   code_includes=None,
+                   outname=None):
     """
     Run a pyplot script and save the images in *output_dir*.
 
@@ -613,6 +635,12 @@ def render_figures(code, code_path, output_dir, output_base, context,
             for fmt, dpi in formats:
                 try:
                     figman.canvas.figure.savefig(img.filename(fmt), dpi=dpi)
+                    if config.plot_cache_dir and outname is not None:
+                        _log.info(
+                            "Preserving '{0}' into '{1}'".format(
+                                img.filename(fmt), config.plot_cache_dir))
+                        shutil.copy2(img.filename(fmt),
+                                     config.plot_cache_dir)
                 except Exception as err:
                     raise PlotError(traceback.format_exc()) from err
                 img.formats.append(fmt)
@@ -648,6 +676,21 @@ def run(arguments, content, options, state_machine, state, lineno):
     rst_file = document.attributes['source']
     rst_dir = os.path.dirname(rst_file)
 
+    # Get output name of the images, if the option was provided
+    outname = options.get('outname', '')
+
+    # Ensure that the outname is unique, otherwise copied images will
+    # not be what user expects
+    if outname and outname in _outname_list:
+        raise Exception("The outname '{0}' is not unique!".format(outname))
+    else:
+        _outname_list.add(outname)
+
+    if config.plot_cache_dir:
+        # Ensure `preserve_dir` ends with a slash, otherwise `copy2`
+        # will misbehave
+        config.plot_cache_dir = os.path.join(config.plot_cache_dir, '')
+
     if len(arguments):
         if not config.plot_basedir:
             source_file_name = os.path.join(setup.app.builder.srcdir,
@@ -693,6 +736,11 @@ def run(arguments, content, options, state_machine, state, lineno):
     else:
         source_ext = ''
 
+    # outname, if present, overrides output_base, but preserve
+    # numbering of multi-figure code snippets
+    if outname:
+        output_base = re.sub('^[^-]*', outname, output_base)
+
     # ensure that LaTeX includegraphics doesn't choke in foo.bar.pdf filenames
     output_base = output_base.replace('.', '-')
 
@@ -753,6 +801,16 @@ def run(arguments, content, options, state_machine, state, lineno):
             else code,
             encoding='utf-8')
 
+    # If we previously preserved copies of the generated figures this copies
+    # them into the build directory so that they will not be remade.
+    if config.plot_cache_dir and outname:
+        outfiles = glob.glob(
+            os.path.join(config.plot_cache_dir, outname) + '*')
+        for of in outfiles:
+            _log.info("Copying preserved copy of '{0}' into '{1}'".format(
+                of, build_dir))
+            shutil.copy2(of, build_dir)
+
     # make figures
     try:
         results = render_figures(code=code,
@@ -764,7 +822,8 @@ def run(arguments, content, options, state_machine, state, lineno):
                                  config=config,
                                  context_reset=context_opt == 'reset',
                                  close_figs=context_opt == 'close-figs',
-                                 code_includes=source_file_includes)
+                                 code_includes=source_file_includes,
+                                 outname=outname)
         errors = []
     except PlotError as err:
         reporter = state.memo.reporter

diff --git a/lib/matplotlib/tests/tinypages/some_plots.rst b/lib/matplotlib/tests/tinypages/some_plots.rst
@@ -174,3 +174,12 @@ Plot 21 is generated via an include directive:
 Plot 22 uses a different specific function in a file with plot commands:
 
 .. plot:: range6.py range10
+
+Plot 23 has an outname
+
+.. plot::
+    :context: close-figs
+    :outname: plot23out
+
+    plt.figure()
+    plt.plot(range(4))