diff --git a/library/std/src/path.rs b/library/std/src/path.rs
index 9d5778ed48cfe..8e918ee2a548b 100644
--- a/library/std/src/path.rs
+++ b/library/std/src/path.rs
@@ -1738,7 +1738,7 @@ impl ToOwned for Path {
 impl cmp::PartialEq for PathBuf {
     #[inline]
     fn eq(&self, other: &PathBuf) -> bool {
-        self.components() == other.components()
+        Path::eq(self, other)
     }
 }
 
@@ -1756,7 +1756,7 @@ impl cmp::Eq for PathBuf {}
 impl cmp::PartialOrd for PathBuf {
     #[inline]
     fn partial_cmp(&self, other: &PathBuf) -> Option<cmp::Ordering> {
-        Some(compare_components(self.components(), other.components()))
+        Path::partial_cmp(self, other)
     }
 }
 
@@ -1764,7 +1764,7 @@ impl cmp::PartialOrd for PathBuf {
 impl cmp::Ord for PathBuf {
     #[inline]
     fn cmp(&self, other: &PathBuf) -> cmp::Ordering {
-        compare_components(self.components(), other.components())
+        Path::cmp(self, other)
     }
 }
 
@@ -2718,6 +2718,33 @@ impl Path {
         let inner = unsafe { Box::from_raw(rw) };
         PathBuf { inner: OsString::from(inner) }
     }
+
+    /// Returns true if the path's syntax indicates it necessarily can only
+    /// refer to a directory.
+    ///
+    /// This is relevant to the PartialEq and PartialOrd impls of Path. For
+    /// example, compared as paths "r/s/" and "r/s/." and "r/s/./" and "r/s/./."
+    /// are all in the same equivalence class, but a different class from "r/s".
+    /// That's because if "r/s" is a file then "r/s" exists while most
+    /// filesystems would consider that "r/s/" does not exist, and thus these
+    /// must not be equal paths.
+    fn syntactically_dir(&self) -> bool {
+        let components = self.components();
+        let bytes_after_prefix =
+            &components.path[components.prefix.as_ref().map_or(0, Prefix::len)..];
+        let mut bytes_iter = bytes_after_prefix.iter();
+        let last_byte = bytes_iter.next_back();
+        let second_last_byte = bytes_iter.next_back();
+        match (second_last_byte, last_byte) {
+            // Path ends in separator, like "path/to/"
+            (_, Some(&sep)) if components.is_sep_byte(sep) => true,
+            // Path ends in separator followed by CurDir, like "path/to/."
+            (Some(&sep), Some(b'.')) if components.is_sep_byte(sep) => true,
+            // Path is ".", because "." and "./." need to be considered equal
+            (None, Some(b'.')) => true,
+            _ => false,
+        }
+    }
 }
 
 #[stable(feature = "rust1", since = "1.0.0")]
@@ -2779,6 +2806,7 @@ impl cmp::PartialEq for Path {
     #[inline]
     fn eq(&self, other: &Path) -> bool {
         self.components() == other.components()
+            && self.syntactically_dir() == other.syntactically_dir()
     }
 }
 
@@ -2798,7 +2826,7 @@ impl cmp::Eq for Path {}
 impl cmp::PartialOrd for Path {
     #[inline]
     fn partial_cmp(&self, other: &Path) -> Option<cmp::Ordering> {
-        Some(compare_components(self.components(), other.components()))
+        Some(Ord::cmp(self, other))
     }
 }
 
@@ -2807,6 +2835,7 @@ impl cmp::Ord for Path {
     #[inline]
     fn cmp(&self, other: &Path) -> cmp::Ordering {
         compare_components(self.components(), other.components())
+            .then_with(|| self.syntactically_dir().cmp(&other.syntactically_dir()))
     }
 }
 
diff --git a/library/std/src/path/tests.rs b/library/std/src/path/tests.rs
index ce23cf6cd21b9..3eaf833dd8423 100644
--- a/library/std/src/path/tests.rs
+++ b/library/std/src/path/tests.rs
@@ -1427,7 +1427,11 @@ pub fn test_compare() {
              let eq = path1 == path2;
              assert!(eq == $eq, "{:?} == {:?}, expected {:?}, got {:?}",
                      $path1, $path2, $eq, eq);
-             assert!($eq == (hash(path1) == hash(path2)),
+
+             // They have the same hash if the paths are equal or differ only in
+             // trailing separator.
+             assert_eq!($eq || $path1.trim_end_matches('/') == $path2.trim_end_matches('/'),
+                     hash(path1) == hash(path2),
                      "{:?} == {:?}, expected {:?}, got {} and {}",
                      $path1, $path2, $eq, hash(path1), hash(path2));
 
@@ -1480,7 +1484,7 @@ pub fn test_compare() {
     );
 
     tc!("foo/", "foo",
-    eq: true,
+    eq: false,
     starts_with: true,
     ends_with: true,
     relative_from: Some("")
@@ -1532,6 +1536,32 @@ pub fn test_compare() {
     }
 }
 
+#[test]
+fn test_trailing_separator() {
+    let file = Path::new("tmp/f");
+    let dir = Path::new("tmp/f/");
+
+    assert_ne!(file, dir);
+    assert!(file < dir);
+    assert_eq!(dir, Path::new("tmp/f//"));
+    assert_eq!(file.components(), dir.components());
+
+    if cfg!(windows) {
+        assert_eq!(dir, Path::new(r"tmp\f\"));
+        assert_eq!(dir, Path::new(r"tmp\f\\"));
+    }
+
+    let dir_dot = Path::new("tmp/f/.");
+    assert_ne!(file, dir_dot);
+    assert!(file < dir_dot);
+    assert_eq!(dir, dir_dot);
+
+    let file = file.to_owned();
+    let dir = dir.to_owned();
+    assert_ne!(file, dir);
+    assert!(file < dir);
+}
+
 #[test]
 fn test_components_debug() {
     let path = Path::new("/tmp");
@@ -1629,10 +1659,19 @@ fn test_ord() {
     ord!(Less, "1", "2");
     ord!(Less, "/foo/bar", "/foo./bar");
     ord!(Less, "foo/bar", "foo/bar.");
-    ord!(Equal, "foo/./bar", "foo/bar/");
-    ord!(Equal, "foo/bar", "foo/bar/");
-    ord!(Equal, "foo/bar", "foo/bar/.");
-    ord!(Equal, "foo/bar", "foo/bar//");
+    ord!(Equal, "foo/./bar", "foo/bar");
+    ord!(Less, "foo/./bar", "foo/bar/");
+    ord!(Equal, "foo/./bar/", "foo/bar/");
+    ord!(Less, "foo/bar", "foo/bar/");
+    ord!(Less, "foo/bar", "foo/bar/.");
+    ord!(Less, "foo/bar", "foo/bar//");
+    ord!(Equal, "foo/bar/", "foo/bar//");
+    ord!(Equal, "foo/bar/", "foo/bar/.");
+    ord!(Equal, "foo/bar/", "foo/bar/./");
+    ord!(Equal, "foo/bar/", "foo/bar/./.");
+    ord!(Less, "/", "./");
+    ord!(Equal, ".", "./");
+    ord!(Equal, ".", "./.");
 }
 
 #[bench]