diff --git a/datafusion/expr/src/udf.rs b/datafusion/expr/src/udf.rs
index dcb942e65b91..f3cc62014486 100644
--- a/datafusion/expr/src/udf.rs
+++ b/datafusion/expr/src/udf.rs
@@ -67,14 +67,31 @@ impl PartialEq for ScalarUDF {
     }
 }
 
-// TODO (https://github.com/apache/datafusion/issues/17064) PartialOrd is not consistent with PartialEq for `ScalarUDF` and it should be
-// Manual implementation based on `ScalarUDFImpl::equals`
 impl PartialOrd for ScalarUDF {
     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
-        match self.name().partial_cmp(other.name()) {
-            Some(Ordering::Equal) => self.signature().partial_cmp(other.signature()),
-            cmp => cmp,
+        let mut cmp = self.name().cmp(other.name());
+        if cmp == Ordering::Equal {
+            cmp = self.signature().partial_cmp(other.signature())?;
         }
+        if cmp == Ordering::Equal {
+            cmp = self.aliases().partial_cmp(other.aliases())?;
+        }
+        // Contract for PartialOrd and PartialEq consistency requires that
+        // a == b if and only if partial_cmp(a, b) == Some(Equal).
+        if cmp == Ordering::Equal && self != other {
+            // Functions may have other properties besides name and signature
+            // that differentiate two instances (e.g. type, or arbitrary parameters).
+            // We cannot return Some(Equal) in such case.
+            return None;
+        }
+        debug_assert!(
+            cmp == Ordering::Equal || self != other,
+            "Detected incorrect implementation of PartialEq when comparing functions: '{}' and '{}'. \
+            The functions compare as equal, but they are not equal based on general properties that \
+            the PartialOrd implementation observes,",
+            self.name(), other.name()
+        );
+        Some(cmp)
     }
 }
 
@@ -942,11 +959,14 @@ The following regular expression functions are supported:"#,
 #[cfg(test)]
 mod tests {
     use super::*;
+    use datafusion_expr_common::signature::Volatility;
     use std::hash::DefaultHasher;
 
     #[derive(Debug, PartialEq, Eq, Hash)]
     struct TestScalarUDFImpl {
+        name: &'static str,
         field: &'static str,
+        signature: Signature,
     }
     impl ScalarUDFImpl for TestScalarUDFImpl {
         fn as_any(&self) -> &dyn Any {
@@ -954,11 +974,11 @@ mod tests {
         }
 
         fn name(&self) -> &str {
-            "TestScalarUDFImpl"
+            self.name
         }
 
         fn signature(&self) -> &Signature {
-            unimplemented!()
+            &self.signature
         }
 
         fn return_type(&self, _arg_types: &[DataType]) -> Result<DataType> {
@@ -970,17 +990,43 @@ mod tests {
         }
     }
 
+    // PartialEq and Hash must be consistent, and also PartialEq and PartialOrd
+    // must be consistent, so they are tested together.
     #[test]
-    fn test_partial_eq() {
-        let a1 = ScalarUDF::from(TestScalarUDFImpl { field: "a" });
-        let a2 = ScalarUDF::from(TestScalarUDFImpl { field: "a" });
-        let b = ScalarUDF::from(TestScalarUDFImpl { field: "b" });
-        let eq = a1 == a2;
-        assert!(eq);
-        assert_eq!(a1, a2);
-        assert_eq!(hash(&a1), hash(&a2));
-        assert_ne!(a1, b);
-        assert_ne!(a2, b);
+    fn test_partial_eq_hash_and_partial_ord() {
+        // A parameterized function
+        let f = test_func("foo", "a");
+
+        // Same like `f`, different instance
+        let f2 = test_func("foo", "a");
+        assert_eq!(f, f2);
+        assert_eq!(hash(&f), hash(&f2));
+        assert_eq!(f.partial_cmp(&f2), Some(Ordering::Equal));
+
+        // Different parameter
+        let b = test_func("foo", "b");
+        assert_ne!(f, b);
+        assert_ne!(hash(&f), hash(&b)); // hash can collide for different values but does not collide in this test
+        assert_eq!(f.partial_cmp(&b), None);
+
+        // Different name
+        let o = test_func("other", "a");
+        assert_ne!(f, o);
+        assert_ne!(hash(&f), hash(&o)); // hash can collide for different values but does not collide in this test
+        assert_eq!(f.partial_cmp(&o), Some(Ordering::Less));
+
+        // Different name and parameter
+        assert_ne!(b, o);
+        assert_ne!(hash(&b), hash(&o)); // hash can collide for different values but does not collide in this test
+        assert_eq!(b.partial_cmp(&o), Some(Ordering::Less));
+    }
+
+    fn test_func(name: &'static str, parameter: &'static str) -> ScalarUDF {
+        ScalarUDF::from(TestScalarUDFImpl {
+            name,
+            field: parameter,
+            signature: Signature::any(1, Volatility::Immutable),
+        })
     }
 
     fn hash<T: Hash>(value: &T) -> u64 {