diff --git a/Library/Homebrew/patch.rb b/Library/Homebrew/patch.rb
index 39e67b1d240316..0894262ac80976 100644
--- a/Library/Homebrew/patch.rb
+++ b/Library/Homebrew/patch.rb
@@ -94,7 +94,7 @@ def contents
   end
 end
 
-# A string containing a patch.
+# A file containing a patch.
 class ExternalPatch
   extend Forwardable
 
@@ -140,7 +140,13 @@ def apply
         patch_files.each do |patch_file|
           ohai "Applying #{patch_file}"
           patch_file = patch_dir/patch_file
-          safe_system "patch", "-g", "0", "-f", "-#{strip}", "-i", patch_file
+          args = %W[-g 0 -f -#{strip}]
+          Utils.safe_popen_write("patch", *args) do |p|
+            File.foreach(patch_file) do |line|
+              data = line.gsub("HOMEBREW_PREFIX", HOMEBREW_PREFIX)
+              p.write(data)
+            end
+          end
         end
       end
     end
diff --git a/Library/Homebrew/test/patching_spec.rb b/Library/Homebrew/test/patching_spec.rb
index 74171d053528e2..d9b8623e54c6e8 100644
--- a/Library/Homebrew/test/patching_spec.rb
+++ b/Library/Homebrew/test/patching_spec.rb
@@ -11,11 +11,13 @@
       TESTBALL_PATCHES_URL = "file://#{TEST_FIXTURE_DIR}/tarballs/testball-0.1-patches.tgz".freeze
       PATCH_URL_A = "file://#{TEST_FIXTURE_DIR}/patches/noop-a.diff".freeze
       PATCH_URL_B = "file://#{TEST_FIXTURE_DIR}/patches/noop-b.diff".freeze
+      PATCH_URL_D = "file://#{TEST_FIXTURE_DIR}/patches/noop-d.diff".freeze
       PATCH_A_CONTENTS = File.read("#{TEST_FIXTURE_DIR}/patches/noop-a.diff").freeze
       PATCH_B_CONTENTS = File.read("#{TEST_FIXTURE_DIR}/patches/noop-b.diff").freeze
       APPLY_A = "noop-a.diff"
       APPLY_B = "noop-b.diff"
       APPLY_C = "noop-c.diff"
+      APPLY_D = "noop-d.diff"
       # rubocop:enable RSpec/LeakyConstantDeclaration,Lint/ConstantDefinitionInBlock
 
       url TESTBALL_URL
@@ -39,6 +41,17 @@ def formula(name = "formula_name", path: Formulary.core_path(name), spec: :stabl
     end
   end
 
+  matcher :be_patched_with_homebrew_prefix do
+    match do |formula|
+      formula.brew do
+        formula.patch
+        s = File.read("libexec/NOOP")
+        expect(s).not_to include("NOOP"), "libexec/NOOP was not patched as expected"
+        expect(s).to include(HOMEBREW_PREFIX.to_s), "libexec/NOOP was not patched as expected"
+      end
+    end
+  end
+
   matcher :have_its_resource_patched do
     match do |formula|
       formula.brew do
@@ -226,6 +239,17 @@ def formula(name = "formula_name", path: Formulary.core_path(name), spec: :stabl
       end
 
       f.brew { |formula, _staging| formula.patch }
-    end.to raise_error(BuildError)
+    end.to raise_error(Errno::ENOENT)
+  end
+
+  specify "patch_dsl_with_homebrew_prefix" do
+    expect(
+      formula do
+        patch do
+          url PATCH_URL_D
+          sha256 PATCH_D_SHA256
+        end
+      end,
+    ).to be_patched_with_homebrew_prefix
   end
 end
diff --git a/Library/Homebrew/test/support/lib/startup/config.rb b/Library/Homebrew/test/support/lib/startup/config.rb
index 8bbba31ea374c3..0b64947dd96090 100644
--- a/Library/Homebrew/test/support/lib/startup/config.rb
+++ b/Library/Homebrew/test/support/lib/startup/config.rb
@@ -47,5 +47,6 @@
 TESTBALL_PATCHES_SHA256 = "799c2d551ac5c3a5759bea7796631a7906a6a24435b52261a317133a0bfb34d9"
 PATCH_A_SHA256 = "83404f4936d3257e65f176c4ffb5a5b8d6edd644a21c8d8dcc73e22a6d28fcfa"
 PATCH_B_SHA256 = "57958271bb802a59452d0816e0670d16c8b70bdf6530bcf6f78726489ad89b90"
+PATCH_D_SHA256 = "29946529088576919b0a56146c346e63692832ab3568cc34fed647c3e4dc2072"
 
 TEST_SHA256 = "deadbeefdeadbeefdeadbeefdeadbeefdeadbeefdeadbeefdeadbeefdeadbeef"
diff --git a/docs/Formula-Cookbook.md b/docs/Formula-Cookbook.md
index e784152cd031db..a4073ab4ae8f7a 100644
--- a/docs/Formula-Cookbook.md
+++ b/docs/Formula-Cookbook.md
@@ -639,7 +639,7 @@ Patches can also be embedded by passing a string. This makes it possible to prov
 patch :p0, "..."
 ```
 
-In embedded patches, the string "HOMEBREW\_PREFIX" is replaced with the value of the constant `HOMEBREW_PREFIX` before the patch is applied.
+In patches, the string "HOMEBREW\_PREFIX" is replaced with the value of the constant `HOMEBREW_PREFIX` before the patch is applied.
 
 ### Creating the diff