diff --git a/promql/engine.go b/promql/engine.go
index d9841295b0..d75f3cae11 100644
--- a/promql/engine.go
+++ b/promql/engine.go
@@ -1545,8 +1545,8 @@ func resultMetric(lhs, rhs labels.Labels, op ItemType, matching *VectorMatching,
 	}
 
 	var lb *labels.Builder
-	if matching.Card == CardOneToMany {
-		// Choose the rhs metric because lhs and rhs have been swapped.
+	if matching.Card == CardOneToMany && op.isComparisonOperator() {
+		// Choose the rhs metric as the one to output because lhs and rhs have been swapped.
 		lb = labels.NewBuilder(rhs)
 	} else {
 		lb = labels.NewBuilder(lhs)
@@ -1556,6 +1556,22 @@ func resultMetric(lhs, rhs labels.Labels, op ItemType, matching *VectorMatching,
 		lb.Del(labels.MetricName)
 	}
 
+	if matching.Card == CardOneToOne && !op.isComparisonOperator() {
+		if matching.On {
+		Outer:
+			for _, l := range lhs {
+				for _, n := range matching.MatchingLabels {
+					if l.Name == n {
+						continue Outer
+					}
+				}
+				lb.Del(l.Name)
+			}
+		} else {
+			lb.Del(matching.MatchingLabels...)
+		}
+	}
+
 	for _, ln := range matching.Include {
 		// Included labels from the `group_x` modifier are taken from the "one"-side.
 		if v := rhs.Get(ln); v != "" {
diff --git a/promql/testdata/operators.test b/promql/testdata/operators.test
index a39f0f11e6..29f8d8fa25 100644
--- a/promql/testdata/operators.test
+++ b/promql/testdata/operators.test
@@ -176,10 +176,10 @@ eval instant at 50m http_requests{group="canary"} unless on(job, instance) http_
 	http_requests{group="canary", instance="1", job="app-server"} 800
 
 eval instant at 50m http_requests{group="canary"} / on(instance,job) http_requests{group="production"}
-	{group="canary", instance="0", job="api-server"} 3
-	{group="canary", instance="0", job="app-server"} 1.4
-	{group="canary", instance="1", job="api-server"} 2
-	{group="canary", instance="1", job="app-server"} 1.3333333333333333
+	{instance="0", job="api-server"} 3
+	{instance="0", job="app-server"} 1.4
+	{instance="1", job="api-server"} 2
+	{instance="1", job="app-server"} 1.3333333333333333
 
 eval instant at 50m http_requests{group="canary"} unless ignoring(group, instance) http_requests{instance="0"}
 
@@ -188,10 +188,10 @@ eval instant at 50m http_requests{group="canary"} unless ignoring(group) http_re
 	http_requests{group="canary", instance="1", job="app-server"} 800
 
 eval instant at 50m http_requests{group="canary"} / ignoring(group) http_requests{group="production"}
-	{group="canary", instance="0", job="api-server"} 3
-	{group="canary", instance="0", job="app-server"} 1.4
-	{group="canary", instance="1", job="api-server"} 2
-	{group="canary", instance="1", job="app-server"} 1.3333333333333333
+	{instance="0", job="api-server"} 3
+	{instance="0", job="app-server"} 1.4
+	{instance="1", job="api-server"} 2
+	{instance="1", job="app-server"} 1.3333333333333333
 
 # https://github.com/prometheus/prometheus/issues/1489
 eval instant at 50m http_requests AND ON (dummy) vector(1)
@@ -398,7 +398,7 @@ load 5m
 
 # On with no labels, for metrics with no common labels.
 eval instant at 5m random + on() metricA
-  {foo="bar"} 5
+  {} 5
 
 # Ignoring with no labels is the same as no ignoring.
 eval instant at 5m metricA + ignoring() metricB