diff --git a/Library/Homebrew/livecheck/strategy.rb b/Library/Homebrew/livecheck/strategy.rb
index 4115432951..f368479843 100644
--- a/Library/Homebrew/livecheck/strategy.rb
+++ b/Library/Homebrew/livecheck/strategy.rb
@@ -80,6 +80,20 @@ module Homebrew
           (strategy.const_defined?(:PRIORITY) ? -strategy::PRIORITY : -DEFAULT_PRIORITY)
         end
       end
+
+      def self.page_headers(url)
+        @headers ||= {}
+        @headers[url] ||= curl_output("--head", "--location", url).stdout
+                                                                  .split("\r\n\r\n", 2).first
+                                                                  .split("\r\n").drop(1)
+                                                                  .map { |header| header.split(/:\s*/, 2) }
+                                                                  .to_h.transform_keys(&:downcase)
+      end
+
+      def self.page_contents(url)
+        @page_contents ||= {}
+        @page_contents[url] ||= URI.parse(url).open.read
+      end
     end
   end
 end
diff --git a/Library/Homebrew/livecheck/strategy/page_match.rb b/Library/Homebrew/livecheck/strategy/page_match.rb
index 49961eff59..478fa2bcda 100644
--- a/Library/Homebrew/livecheck/strategy/page_match.rb
+++ b/Library/Homebrew/livecheck/strategy/page_match.rb
@@ -30,8 +30,8 @@ module Homebrew
         URL_MATCH_REGEX = %r{^https?://}i.freeze
 
         # Whether the strategy can be applied to the provided URL.
-        # PageMatch will technically match any HTTP URL but it's only usable
-        # when the formula has a `livecheck` block containing a regex.
+        # PageMatch will technically match any HTTP URL but is only
+        # usable with a `livecheck` block containing a regex.
         #
         # @param url [String] the URL to match against
         # @return [Boolean]
@@ -47,9 +47,8 @@ module Homebrew
         #   content
         # @return [Array]
         def self.page_matches(url, regex)
-          page = URI.parse(url).open.read
-          matches = page.scan(regex)
-          matches.map(&:first).uniq
+          page = Strategy.page_contents(url)
+          page.scan(regex).map(&:first).uniq
         end
 
         # Checks the content at the URL for new versions, using the provided