diff --git a/lib/elixir/lib/task.ex b/lib/elixir/lib/task.ex
index ef7af6ebd7a..ec881c4450a 100644
--- a/lib/elixir/lib/task.ex
+++ b/lib/elixir/lib/task.ex
@@ -1444,6 +1444,13 @@ defmodule Task do
     end
   end
 
+  # exported only to avoid dialyzer opaqueness check in internal Task modules
+  @doc false
+  @spec __alias__(pid()) :: Task.ref()
+  def __alias__(pid) do
+    build_alias(pid)
+  end
+
   ## Optimizations
 
   defp build_monitor(pid) do
diff --git a/lib/elixir/lib/task/supervisor.ex b/lib/elixir/lib/task/supervisor.ex
index 59b63f680e0..a296e9bfe03 100644
--- a/lib/elixir/lib/task/supervisor.ex
+++ b/lib/elixir/lib/task/supervisor.ex
@@ -614,7 +614,7 @@ defmodule Task.Supervisor do
     case start_child_with_spec(supervisor, [get_owner(owner), :monitor], :temporary, shutdown) do
       {:ok, pid} ->
         if link_type == :link, do: Process.link(pid)
-        alias = :erlang.monitor(:process, pid, alias: :demonitor)
+        alias = Task.__alias__(pid)
         send(pid, {owner, alias, alias, get_callers(owner), {module, fun, args}})
         %Task{pid: pid, ref: alias, owner: owner, mfa: {module, fun, length(args)}}
 
diff --git a/lib/elixir/test/elixir/fixtures/dialyzer/opaque_inline.ex b/lib/elixir/test/elixir/fixtures/dialyzer/opaque_inline.ex
deleted file mode 100644
index ce224ee523b..00000000000
--- a/lib/elixir/test/elixir/fixtures/dialyzer/opaque_inline.ex
+++ /dev/null
@@ -1,10 +0,0 @@
-defmodule Dialyzer.OpaqueInline do
-  @spec bar(MapSet.t()) :: term()
-  def bar(set) do
-    set
-  end
-
-  def foo() do
-    bar(MapSet.new([1, 2, 3]))
-  end
-end
diff --git a/lib/elixir/test/elixir/fixtures/dialyzer/opaqueness.ex b/lib/elixir/test/elixir/fixtures/dialyzer/opaqueness.ex
new file mode 100644
index 00000000000..12857f515fe
--- /dev/null
+++ b/lib/elixir/test/elixir/fixtures/dialyzer/opaqueness.ex
@@ -0,0 +1,17 @@
+defmodule Dialyzer.Opaqueness do
+  @spec bar(MapSet.t()) :: term()
+  def bar(set) do
+    set
+  end
+
+  def foo() do
+    # inlining of literals should not violate opaqueness check
+    bar(MapSet.new([1, 2, 3]))
+  end
+
+  # Task.Supervisor returns a Task.t() containing an opaque Task.ref()
+  @spec run_task() :: Task.t()
+  def run_task do
+    Task.Supervisor.async(SupervisorName, fn -> :ok end)
+  end
+end
diff --git a/lib/elixir/test/elixir/kernel/dialyzer_test.exs b/lib/elixir/test/elixir/kernel/dialyzer_test.exs
index 615f946b0d9..01aa977ecae 100644
--- a/lib/elixir/test/elixir/kernel/dialyzer_test.exs
+++ b/lib/elixir/test/elixir/kernel/dialyzer_test.exs
@@ -50,7 +50,9 @@ defmodule Kernel.DialyzerTest do
       Module,
       Protocol,
       String,
-      String.Chars
+      String.Chars,
+      Task,
+      Task.Supervisor
     ]
 
     files = Enum.map(mods, &:code.which/1)
@@ -178,8 +180,8 @@ defmodule Kernel.DialyzerTest do
     assert_dialyze_no_warnings!(context)
   end
 
-  test "no warning on inlined calls returning opaque", context do
-    copy_beam!(context, Dialyzer.OpaqueInline)
+  test "no warning due to opaqueness edge cases", context do
+    copy_beam!(context, Dialyzer.Opaqueness)
     assert_dialyze_no_warnings!(context)
   end