diff --git a/Library/Homebrew/cask/lib/hbc/installer.rb b/Library/Homebrew/cask/lib/hbc/installer.rb
index cafc9d8b9e..b86f3264d2 100644
--- a/Library/Homebrew/cask/lib/hbc/installer.rb
+++ b/Library/Homebrew/cask/lib/hbc/installer.rb
@@ -318,7 +318,13 @@ module Hbc
     def uninstall_artifacts
       odebug "Un-installing artifacts"
       artifacts = Artifact.for_cask(@cask, command: @command, force: force)
+
+      # Make sure the `uninstall` stanza is run first, as it
+      # may depend on other artifacts still being installed.
+      artifacts = artifacts.sort_by { |a| a.is_a?(Artifact::Uninstall) ? -1 : 1 }
+
       odebug "#{artifacts.length} artifact/s defined", artifacts
+
       artifacts.each do |artifact|
         next unless artifact.respond_to?(:uninstall_phase)
         odebug "Un-installing artifact of class #{artifact.class}"