diff --git a/clippy_lints/src/minmax.rs b/clippy_lints/src/minmax.rs
index dae39aaf5e21..1f798fd11209 100644
--- a/clippy_lints/src/minmax.rs
+++ b/clippy_lints/src/minmax.rs
@@ -18,6 +18,10 @@ declare_clippy_lint! {
     /// ```ignore
     /// min(0, max(100, x))
     /// ```
+    /// or
+    /// ```ignore
+    /// x.max(100).min(0)
+    /// ```
     /// It will always be equal to `0`. Probably the author meant to clamp the value
     /// between 0 and 100, but has erroneously swapped `min` and `max`.
     pub MIN_MAX,
@@ -60,25 +64,35 @@ enum MinMax {
 }
 
 fn min_max<'a>(cx: &LateContext<'_>, expr: &'a Expr<'a>) -> Option<(MinMax, Constant, &'a Expr<'a>)> {
-    if let ExprKind::Call(ref path, ref args) = expr.kind {
-        if let ExprKind::Path(ref qpath) = path.kind {
-            cx.typeck_results()
-                .qpath_res(qpath, path.hir_id)
-                .opt_def_id()
-                .and_then(|def_id| {
-                    if match_def_path(cx, def_id, &paths::CMP_MIN) {
-                        fetch_const(cx, args, MinMax::Min)
-                    } else if match_def_path(cx, def_id, &paths::CMP_MAX) {
-                        fetch_const(cx, args, MinMax::Max)
-                    } else {
-                        None
-                    }
-                })
-        } else {
-            None
-        }
-    } else {
-        None
+    match expr.kind {
+        ExprKind::Call(ref path, ref args) => {
+            if let ExprKind::Path(ref qpath) = path.kind {
+                cx.typeck_results()
+                    .qpath_res(qpath, path.hir_id)
+                    .opt_def_id()
+                    .and_then(|def_id| {
+                        if match_def_path(cx, def_id, &paths::CMP_MIN) {
+                            fetch_const(cx, args, MinMax::Min)
+                        } else if match_def_path(cx, def_id, &paths::CMP_MAX) {
+                            fetch_const(cx, args, MinMax::Max)
+                        } else {
+                            None
+                        }
+                    })
+            } else {
+                None
+            }
+        },
+        ExprKind::MethodCall(ref path, _, ref args, _) => {
+            if path.ident.as_str() == sym!(max).as_str() {
+                fetch_const(cx, args, MinMax::Max)
+            } else if path.ident.as_str() == sym!(min).as_str() {
+                fetch_const(cx, args, MinMax::Min)
+            } else {
+                None
+            }
+        },
+        _ => None,
     }
 }
 
diff --git a/tests/ui/min_max.rs b/tests/ui/min_max.rs
index 8307d4b3019f..90ec5676493a 100644
--- a/tests/ui/min_max.rs
+++ b/tests/ui/min_max.rs
@@ -30,4 +30,18 @@ fn main() {
     max(min(s, "Apple"), "Zoo");
 
     max("Apple", min(s, "Zoo")); // ok
+
+    x.min(1).max(3);
+    x.max(3).min(1);
+
+    x.max(1).min(3); // ok
+    x.min(3).max(1); // ok
+
+    max(x.min(1), 3);
+    min(x.max(1), 3); // ok
+
+    s.max("Zoo").min("Apple");
+    s.min("Apple").max("Zoo");
+
+    s.min("Zoo").max("Apple"); // ok
 }
diff --git a/tests/ui/min_max.stderr b/tests/ui/min_max.stderr
index b552c137f7c7..653946dc025f 100644
--- a/tests/ui/min_max.stderr
+++ b/tests/ui/min_max.stderr
@@ -42,5 +42,35 @@ error: this `min`/`max` combination leads to constant result
 LL |     max(min(s, "Apple"), "Zoo");
    |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
-error: aborting due to 7 previous errors
+error: this `min`/`max` combination leads to constant result
+  --> $DIR/min_max.rs:34:5
+   |
+LL |     x.min(1).max(3);
+   |     ^^^^^^^^^^^^^^^
+
+error: this `min`/`max` combination leads to constant result
+  --> $DIR/min_max.rs:35:5
+   |
+LL |     x.max(3).min(1);
+   |     ^^^^^^^^^^^^^^^
+
+error: this `min`/`max` combination leads to constant result
+  --> $DIR/min_max.rs:40:5
+   |
+LL |     max(x.min(1), 3);
+   |     ^^^^^^^^^^^^^^^^
+
+error: this `min`/`max` combination leads to constant result
+  --> $DIR/min_max.rs:43:5
+   |
+LL |     s.max("Zoo").min("Apple");
+   |     ^^^^^^^^^^^^^^^^^^^^^^^^^
+
+error: this `min`/`max` combination leads to constant result
+  --> $DIR/min_max.rs:44:5
+   |
+LL |     s.min("Apple").max("Zoo");
+   |     ^^^^^^^^^^^^^^^^^^^^^^^^^
+
+error: aborting due to 12 previous errors