diff --git a/piptools/repositories/local.py b/piptools/repositories/local.py
index e2a96be4d..4cb04178b 100644
--- a/piptools/repositories/local.py
+++ b/piptools/repositories/local.py
@@ -63,9 +63,7 @@ def find_best_match(self, ireq, prereleases=None):
         existing_pin = self.existing_pins.get(key)
         if existing_pin and ireq_satisfied_by_existing_pin(ireq, existing_pin):
             project, version, _ = as_tuple(existing_pin)
-            return make_install_requirement(
-                project, version, ireq.extras, constraint=ireq.constraint
-            )
+            return make_install_requirement(project, version, ireq)
         else:
             return self.repository.find_best_match(ireq, prereleases)
 
diff --git a/piptools/repositories/pypi.py b/piptools/repositories/pypi.py
index 433187dda..d64f48027 100644
--- a/piptools/repositories/pypi.py
+++ b/piptools/repositories/pypi.py
@@ -159,8 +159,7 @@ def find_best_match(self, ireq, prereleases=None):
         return make_install_requirement(
             best_candidate.name,
             best_candidate.version,
-            ireq.extras,
-            constraint=ireq.constraint,
+            ireq,
         )
 
     def resolve_reqs(self, download_dir, ireq, wheel_cache):
diff --git a/piptools/utils.py b/piptools/utils.py
index 5ed2c38b9..cde26a5e1 100644
--- a/piptools/utils.py
+++ b/piptools/utils.py
@@ -21,6 +21,7 @@
 from pip._internal.vcs import is_url
 from pip._vendor.packaging.markers import Marker
 from pip._vendor.packaging.specifiers import SpecifierSet
+from pip._vendor.packaging.version import Version
 
 _KT = TypeVar("_KT")
 _VT = TypeVar("_VT")
@@ -66,16 +67,25 @@ def comment(text: str) -> str:
 
 
 def make_install_requirement(
-    name: str, version: str, extras: Iterable[str], constraint: bool = False
+    name: str, version: Union[str, Version], ireq: InstallRequirement
 ) -> InstallRequirement:
     # If no extras are specified, the extras string is blank
     extras_string = ""
+    extras = ireq.extras
     if extras:
         # Sort extras for stability
         extras_string = f"[{','.join(sorted(extras))}]"
 
+    version_pin_operator = "=="
+    version_as_str = str(version)
+    for specifier in ireq.specifier:
+        if specifier.operator == "===" and specifier.version == version_as_str:
+            version_pin_operator = "==="
+            break
+
     return install_req_from_line(
-        str(f"{name}{extras_string}=={version}"), constraint=constraint
+        str(f"{name}{extras_string}{version_pin_operator}{version}"),
+        constraint=ireq.constraint,
     )
 
 
diff --git a/tests/conftest.py b/tests/conftest.py
index 0936845ed..c7021951c 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -68,9 +68,7 @@ def find_best_match(self, ireq, prereleases=False):
             ]
             raise NoCandidateFound(ireq, tried_versions, ["https://fake.url.foo"])
         best_version = max(versions, key=Version)
-        return make_install_requirement(
-            key_from_ireq(ireq), best_version, ireq.extras, constraint=ireq.constraint
-        )
+        return make_install_requirement(key_from_ireq(ireq), best_version, ireq)
 
     def get_dependencies(self, ireq):
         if ireq.editable or is_url_requirement(ireq):
diff --git a/tests/test_cli_compile.py b/tests/test_cli_compile.py
index 603d3f83f..5f50a27aa 100644
--- a/tests/test_cli_compile.py
+++ b/tests/test_cli_compile.py
@@ -1555,3 +1555,74 @@ def test_duplicate_reqs_combined(
     assert out.exit_code == 0, out
     assert str(test_package_2) in out.stderr
     assert "test-package-1==0.1" in out.stderr
+
+
+@pytest.mark.parametrize(
+    ("pkg2_install_requires", "req_in_content", "out_expected_content"),
+    (
+        pytest.param(
+            "",
+            ["test-package-1===0.1.0\n"],
+            ["test-package-1===0.1.0"],
+            id="pin package with ===",
+        ),
+        pytest.param(
+            "",
+            ["test-package-1==0.1.0\n"],
+            ["test-package-1==0.1.0"],
+            id="pin package with ==",
+        ),
+        pytest.param(
+            "test-package-1==0.1.0",
+            ["test-package-1===0.1.0\n", "test-package-2==0.1.0\n"],
+            ["test-package-1===0.1.0", "test-package-2==0.1.0"],
+            id="dep === pin preferred over == pin, main package == pin",
+        ),
+        pytest.param(
+            "test-package-1==0.1.0",
+            ["test-package-1===0.1.0\n", "test-package-2===0.1.0\n"],
+            ["test-package-1===0.1.0", "test-package-2===0.1.0"],
+            id="dep === pin preferred over == pin, main package === pin",
+        ),
+        pytest.param(
+            "test-package-1==0.1.0",
+            ["test-package-2===0.1.0\n"],
+            ["test-package-1==0.1.0", "test-package-2===0.1.0"],
+            id="dep == pin conserved, main package === pin",
+        ),
+    ),
+)
+def test_triple_equal_pinned_dependency_is_used(
+    runner,
+    make_package,
+    make_wheel,
+    tmpdir,
+    pkg2_install_requires,
+    req_in_content,
+    out_expected_content,
+):
+    """
+    Test that pip-compile properly emits the pinned requirement with ===
+    torchvision 0.8.2 requires torch==1.7.1 which can resolve to versions with
+    patches (e.g. torch 1.7.1+cu110), we want torch===1.7.1 without patches
+    """
+
+    dists_dir = tmpdir / "dists"
+
+    test_package_1 = make_package("test_package_1", version="0.1.0")
+    make_wheel(test_package_1, dists_dir)
+
+    test_package_2 = make_package(
+        "test_package_2", version="0.1.0", install_requires=[pkg2_install_requires]
+    )
+    make_wheel(test_package_2, dists_dir)
+
+    with open("requirements.in", "w") as reqs_in:
+        for line in req_in_content:
+            reqs_in.write(line)
+
+    out = runner.invoke(cli, ["--find-links", str(dists_dir)])
+
+    assert out.exit_code == 0, out
+    for line in out_expected_content:
+        assert line in out.stderr