diff --git a/datafusion/src/optimizer/projection_push_down.rs b/datafusion/src/optimizer/projection_push_down.rs
index a9e571f3d00b..2cd7384e2443 100644
--- a/datafusion/src/optimizer/projection_push_down.rs
+++ b/datafusion/src/optimizer/projection_push_down.rs
@@ -29,7 +29,10 @@ use crate::optimizer::utils;
 use crate::sql::utils::find_sort_exprs;
 use arrow::datatypes::{Field, Schema};
 use arrow::error::Result as ArrowResult;
-use std::{collections::HashSet, sync::Arc};
+use std::{
+    collections::{BTreeSet, HashSet},
+    sync::Arc,
+};
 use utils::optimize_explain;
 
 /// Optimizer that removes unused projections and aggregations from plans
@@ -75,9 +78,12 @@ fn get_projected_schema(
     //
     // we discard non-existing columns because some column names are not part of the schema,
     // e.g. when the column derives from an aggregation
-    let mut projection: Vec<usize> = required_columns
+    //
+    // Use BTreeSet to remove potential duplicates (e.g. union) as
+    // well as to sort the projection to ensure deterministic behavior
+    let mut projection: BTreeSet<usize> = required_columns
         .iter()
-        .filter(|c| c.relation.as_ref() == table_name)
+        .filter(|c| c.relation.is_none() || c.relation.as_ref() == table_name)
         .map(|c| schema.index_of(&c.name))
         .filter_map(ArrowResult::ok)
         .collect();
@@ -87,7 +93,7 @@ fn get_projected_schema(
             // Ensure that we are reading at least one column from the table in case the query
             // does not reference any columns directly such as "SELECT COUNT(1) FROM table",
             // except when the table is empty (no column)
-            projection.push(0);
+            projection.insert(0);
         } else {
             // for table scan without projection, we default to return all columns
             projection = schema
@@ -95,13 +101,10 @@ fn get_projected_schema(
                 .iter()
                 .enumerate()
                 .map(|(i, _)| i)
-                .collect::<Vec<usize>>();
+                .collect::<BTreeSet<usize>>();
         }
     }
 
-    // sort the projection otherwise we get non-deterministic behavior
-    projection.sort_unstable();
-
     // create the projected schema
     let mut projected_fields: Vec<DFField> = Vec::with_capacity(projection.len());
     match table_name {
@@ -120,6 +123,7 @@ fn get_projected_schema(
         }
     }
 
+    let projection = projection.into_iter().collect::<Vec<_>>();
     Ok((projection, projected_fields.to_dfschema_ref()?))
 }
 
@@ -438,7 +442,9 @@ fn optimize_plan(
 mod tests {
 
     use super::*;
-    use crate::logical_plan::{col, lit, max, min, Expr, JoinType, LogicalPlanBuilder};
+    use crate::logical_plan::{
+        col, exprlist_to_fields, lit, max, min, Expr, JoinType, LogicalPlanBuilder,
+    };
     use crate::test::*;
     use arrow::datatypes::DataType;
 
@@ -568,6 +574,35 @@ mod tests {
         Ok(())
     }
 
+    #[test]
+    fn table_scan_projected_schema_non_qualified_relation() -> Result<()> {
+        let table_scan = test_table_scan()?;
+        let input_schema = table_scan.schema();
+        assert_eq!(3, input_schema.fields().len());
+        assert_fields_eq(&table_scan, vec!["a", "b", "c"]);
+
+        // Build the LogicalPlan directly (don't use PlanBuilder), so
+        // that the Column references are unqualified (e.g. their
+        // relation is `None`). PlanBuilder resolves the expressions
+        let expr = vec![col("a"), col("b")];
+        let projected_fields = exprlist_to_fields(&expr, input_schema).unwrap();
+        let projected_schema = DFSchema::new(projected_fields).unwrap();
+        let plan = LogicalPlan::Projection {
+            expr,
+            input: Arc::new(table_scan),
+            schema: Arc::new(projected_schema),
+        };
+
+        assert_fields_eq(&plan, vec!["a", "b"]);
+
+        let expected = "Projection: #a, #b\
+        \n  TableScan: test projection=Some([0, 1])";
+
+        assert_optimized_plan_eq(&plan, expected);
+
+        Ok(())
+    }
+
     #[test]
     fn table_limit() -> Result<()> {
         let table_scan = test_table_scan()?;