diff --git a/Lib/logging/handlers.py b/Lib/logging/handlers.py
index 7f1f10551c3040..f8040c498c10de 100644
--- a/Lib/logging/handlers.py
+++ b/Lib/logging/handlers.py
@@ -368,8 +368,13 @@ def getFilesToDelete(self):
         for fileName in fileNames:
             if fileName[:plen] == prefix:
                 suffix = fileName[plen:]
-                if self.extMatch.match(suffix):
-                    result.append(os.path.join(dirName, fileName))
+                # See bpo-45628: The date/time suffix could be anywhere in the
+                # filename
+                parts = suffix.split('.')
+                for part in parts:
+                    if self.extMatch.match(part):
+                        result.append(os.path.join(dirName, fileName))
+                        break
         if len(result) < self.backupCount:
             result = []
         else: