diff --git a/Library/Homebrew/brew.sh b/Library/Homebrew/brew.sh
index 069c8b7d8f..273454dcfc 100644
--- a/Library/Homebrew/brew.sh
+++ b/Library/Homebrew/brew.sh
@@ -290,11 +290,31 @@ auto-update() {
       fi
     fi
 
-    # Skip auto-update if the Homebrew/brew repository has been checked in the
+    repo_fetch_heads=("${HOMEBREW_REPOSITORY}/.git/FETCH_HEAD")
+    # We might have done an auto-update recently, but not a core/cask clone auto-update.
+    # So we check the core/cask clone FETCH_HEAD too.
+    if [[ -n "${HOMEBREW_UPDATE_CORE_TAP}" && -d "${HOMEBREW_CORE_REPOSITORY}/.git" ]]
+    then
+      repo_fetch_heads+=("${HOMEBREW_CORE_REPOSITORY}/.git/FETCH_HEAD")
+    fi
+    if [[ -n "${HOMEBREW_UPDATE_CASK_TAP}" && -d "${HOMEBREW_CASK_REPOSITORY}/.git" ]]
+    then
+      repo_fetch_heads+=("${HOMEBREW_CASK_REPOSITORY}/.git/FETCH_HEAD")
+    fi
+
+    # Skip auto-update if all of the selected repositories have been checked in the
     # last $HOMEBREW_AUTO_UPDATE_SECS.
-    repo_fetch_head="${HOMEBREW_REPOSITORY}/.git/FETCH_HEAD"
-    if [[ -f "${repo_fetch_head}" ]] &&
-       [[ -n "$(find "${repo_fetch_head}" -type f -mtime -"${HOMEBREW_AUTO_UPDATE_SECS}"s 2>/dev/null)" ]]
+    needs_auto_update=
+    for repo_fetch_head in "${repo_fetch_heads[@]}"
+    do
+      if [[ ! -f "${repo_fetch_head}" ]] ||
+         [[ -z "$(find "${repo_fetch_head}" -type f -mtime -"${HOMEBREW_AUTO_UPDATE_SECS}"s 2>/dev/null)" ]]
+      then
+        needs_auto_update=1
+        break
+      fi
+    done
+    if [[ -z "${needs_auto_update}" ]]
     then
       return
     fi
@@ -323,6 +343,10 @@ auto-update() {
   fi
 
   unset AUTO_UPDATE_COMMANDS
+  unset AUTO_UPDATE_CORE_TAP_COMMANDS
+  unset AUTO_UPDATE_CASK_TAP_COMMANDS
+  unset HOMEBREW_UPDATE_CORE_TAP
+  unset HOMEBREW_UPDATE_CASK_TAP
 }
 
 #####
@@ -807,13 +831,13 @@ then
   unset HOMEBREW_RUBY_WARNINGS
 fi
 
+unset HOMEBREW_AUTO_UPDATE_COMMAND
+
 # Check for commands that should call `brew update --auto-update` first.
 AUTO_UPDATE_COMMANDS=(
   install
   outdated
   upgrade
-  bump-formula-pr
-  bump-cask-pr
   bundle
   release
 )
@@ -823,6 +847,28 @@ then
   export HOMEBREW_AUTO_UPDATE_COMMAND="1"
 fi
 
+# Check for commands that should auto-update the homebrew-core tap.
+AUTO_UPDATE_CORE_TAP_COMMANDS=(
+  bump
+  bump-formula-pr
+)
+if check-array-membership "${HOMEBREW_COMMAND}" "${AUTO_UPDATE_CORE_TAP_COMMANDS[@]}"
+then
+  export HOMEBREW_AUTO_UPDATE_COMMAND="1"
+  export HOMEBREW_UPDATE_CORE_TAP="1"
+fi
+
+# Check for commands that should auto-update the homebrew-cask tap.
+AUTO_UPDATE_CASK_TAP_COMMANDS=(
+  bump
+  bump-cask-pr
+)
+if check-array-membership "${HOMEBREW_COMMAND}" "${AUTO_UPDATE_CASK_TAP_COMMANDS[@]}"
+then
+  export HOMEBREW_AUTO_UPDATE_COMMAND="1"
+  export HOMEBREW_UPDATE_CASK_TAP="1"
+fi
+
 # Disable Ruby options we don't need.
 export HOMEBREW_RUBY_DISABLE_OPTIONS="--disable=gems,rubyopt"
 
diff --git a/Library/Homebrew/cmd/update.sh b/Library/Homebrew/cmd/update.sh
index f319b5be69..3617a8ec32 100644
--- a/Library/Homebrew/cmd/update.sh
+++ b/Library/Homebrew/cmd/update.sh
@@ -575,7 +575,8 @@ EOS
   for DIR in "${HOMEBREW_REPOSITORY}" "${HOMEBREW_LIBRARY}"/Taps/*/*
   do
     if [[ -z "${HOMEBREW_NO_INSTALL_FROM_API}" && -n "${HOMEBREW_UPDATE_AUTO}" ]] &&
-       [[ "${DIR}" == "${HOMEBREW_CORE_REPOSITORY}" || "${DIR}" == "${HOMEBREW_CASK_REPOSITORY}" ]]
+       [[ ("${DIR}" == "${HOMEBREW_CORE_REPOSITORY}" && -z "${HOMEBREW_UPDATE_CORE_TAP}") ||
+          ("${DIR}" == "${HOMEBREW_CASK_REPOSITORY}" && -z "${HOMEBREW_UPDATE_CASK_TAP}") ]]
     then
       continue
     fi
@@ -731,8 +732,8 @@ EOS
   do
     if [[ -z "${HOMEBREW_NO_INSTALL_FROM_API}" ]] &&
        [[ -z "${HOMEBREW_DEVELOPER}" || -n "${HOMEBREW_UPDATE_AUTO}" ]] &&
-       [[ "${DIR}" == "${HOMEBREW_CORE_REPOSITORY}" ||
-          "${DIR}" == "${HOMEBREW_CASK_REPOSITORY}" ]]
+       [[ ("${DIR}" == "${HOMEBREW_CORE_REPOSITORY}" && -z "${HOMEBREW_UPDATE_CORE_TAP}") ||
+          ("${DIR}" == "${HOMEBREW_CASK_REPOSITORY}" && -z "${HOMEBREW_UPDATE_CASK_TAP}") ]]
     then
       continue
     fi