diff --git a/lib/matplotlib/backends/backend_qt5.py b/lib/matplotlib/backends/backend_qt5.py
index 2685ab5b677a..6fc86486183c 100644
--- a/lib/matplotlib/backends/backend_qt5.py
+++ b/lib/matplotlib/backends/backend_qt5.py
@@ -17,7 +17,8 @@
 from matplotlib.backend_managers import ToolManager
 
 from .qt_compat import (
-    QtCore, QtGui, QtWidgets, _getSaveFileName, is_pyqt5, __version__, QT_API)
+    QtCore, QtGui, QtWidgets, _isdeleted, _getSaveFileName,
+    is_pyqt5, __version__, QT_API)
 
 backend_version = __version__
 
@@ -200,6 +201,12 @@ def __init__(self, *args, **kwargs):
         self._timer.timeout.connect(self._on_timer)
         self._timer_set_interval()
 
+    def __del__(self):
+        # The check for deletedness is needed to avoid an error at animation
+        # shutdown with PySide2.
+        if not _isdeleted(self._timer):
+            self._timer_stop()
+
     def _timer_set_single_shot(self):
         self._timer.setSingleShot(self._single)
 
diff --git a/lib/matplotlib/backends/qt_compat.py b/lib/matplotlib/backends/qt_compat.py
index 6b52284fe7f4..b3367ea91010 100644
--- a/lib/matplotlib/backends/qt_compat.py
+++ b/lib/matplotlib/backends/qt_compat.py
@@ -63,16 +63,21 @@
 
 
 def _setup_pyqt5():
-    global QtCore, QtGui, QtWidgets, __version__, is_pyqt5, _getSaveFileName
+    global QtCore, QtGui, QtWidgets, __version__, is_pyqt5, \
+        _isdeleted, _getSaveFileName
 
     if QT_API == QT_API_PYQT5:
         from PyQt5 import QtCore, QtGui, QtWidgets
+        import sip
         __version__ = QtCore.PYQT_VERSION_STR
         QtCore.Signal = QtCore.pyqtSignal
         QtCore.Slot = QtCore.pyqtSlot
         QtCore.Property = QtCore.pyqtProperty
+        _isdeleted = sip.isdeleted
     elif QT_API == QT_API_PYSIDE2:
         from PySide2 import QtCore, QtGui, QtWidgets, __version__
+        import shiboken2
+        def _isdeleted(obj): return not shiboken2.isValid(obj)
     else:
         raise ValueError("Unexpected value for the 'backend.qt5' rcparam")
     _getSaveFileName = QtWidgets.QFileDialog.getSaveFileName
@@ -82,7 +87,8 @@ def is_pyqt5():
 
 
 def _setup_pyqt4():
-    global QtCore, QtGui, QtWidgets, __version__, is_pyqt5, _getSaveFileName
+    global QtCore, QtGui, QtWidgets, __version__, is_pyqt5, \
+        _isdeleted, _getSaveFileName
 
     def _setup_pyqt4_internal(api):
         global QtCore, QtGui, QtWidgets, \
@@ -102,6 +108,7 @@ def _setup_pyqt4_internal(api):
                 except ValueError:
                     pass
         from PyQt4 import QtCore, QtGui
+        import sip  # Always succeeds *after* importing PyQt4.
         __version__ = QtCore.PYQT_VERSION_STR
         # PyQt 4.6 introduced getSaveFileNameAndFilter:
         # https://riverbankcomputing.com/news/pyqt-46
@@ -110,16 +117,19 @@ def _setup_pyqt4_internal(api):
         QtCore.Signal = QtCore.pyqtSignal
         QtCore.Slot = QtCore.pyqtSlot
         QtCore.Property = QtCore.pyqtProperty
+        _isdeleted = sip.isdeleted
         _getSaveFileName = QtGui.QFileDialog.getSaveFileNameAndFilter
 
     if QT_API == QT_API_PYQTv2:
         _setup_pyqt4_internal(api=2)
     elif QT_API == QT_API_PYSIDE:
         from PySide import QtCore, QtGui, __version__, __version_info__
+        import shiboken
         # PySide 1.0.3 fixed the following:
         # https://srinikom.github.io/pyside-bz-archive/809.html
         if __version_info__ < (1, 0, 3):
             raise ImportError("PySide<1.0.3 is not supported")
+        def _isdeleted(obj): return not shiboken.isValid(obj)
         _getSaveFileName = QtGui.QFileDialog.getSaveFileName
     elif QT_API == QT_API_PYQT:
         _setup_pyqt4_internal(api=1)