diff --git a/asyncstdlib/builtins.py b/asyncstdlib/builtins.py
index 5c8f54c..0ea160c 100644
--- a/asyncstdlib/builtins.py
+++ b/asyncstdlib/builtins.py
@@ -312,14 +312,14 @@ async def _min_max(
             raise ValueError(f"{name}() arg is an empty sequence")
         elif key is None:
             async for item in item_iter:
-                if invert ^ bool(item < best):
+                if best < item if invert else item < best:
                     best = item
         else:
             key = _awaitify(key)
             best_key = await key(best)
             async for item in item_iter:
                 item_key = await key(item)
-                if invert ^ (item_key < best_key):
+                if best_key < item_key if invert else item_key < best_key:
                     best = item
                     best_key = item_key
     return best
diff --git a/unittests/test_builtins.py b/unittests/test_builtins.py
index 382fddd..e11fb27 100644
--- a/unittests/test_builtins.py
+++ b/unittests/test_builtins.py
@@ -1,4 +1,5 @@
 import random
+from functools import total_ordering
 from typing import Any, Callable, Coroutine, TypeVar
 
 import pytest
@@ -343,3 +344,47 @@ def collision_key(x: int) -> int:
     assert await a.sorted(values, key=awaitify(collision_key)) == sorted(
         values, key=collision_key
     )
+
+
+@total_ordering
+class ComparableRecord:
+    def __init__(self, priority):
+        self.priority = priority
+
+    def __eq__(self, other):
+        if not isinstance(other, ComparableRecord):
+            return NotImplemented
+        return self.priority == other.priority
+
+    def __lt__(self, other):
+        if not isinstance(other, ComparableRecord):
+            return NotImplemented
+        return self.priority < other.priority
+
+
+def record_priority(record):
+    return record.priority
+
+
+@pytest.mark.parametrize(
+    "key, reference_key",
+    [
+        (None, None),
+        (record_priority, record_priority),
+        (awaitify(record_priority), record_priority),
+    ],
+)
+@pytest.mark.parametrize("iterable", [iter, asyncify])
+@sync
+async def test_max_keeps_first_equal_item(key, reference_key, iterable):
+    values = [ComparableRecord(value) for value in (1, 3, 3, 2)]
+    assert await a.max(iterable(values), key=key) is max(values, key=reference_key)
+
+
+@pytest.mark.parametrize(
+    "values",
+    [[float("nan"), 3.0], [3.0, float("nan"), 2.0], [2.0, float("nan"), 3.0]],
+)
+@sync
+async def test_max_does_not_replace_with_unordered_values(values):
+    assert await a.max(asyncify(values)) is max(values)