diff --git a/promql/bench_test.go b/promql/bench_test.go
index 8abfcfdd2..88025d932 100644
--- a/promql/bench_test.go
+++ b/promql/bench_test.go
@@ -157,6 +157,9 @@ func rangeQueryCases() []benchCase {
 		{
 			expr: "topk(1, a_X)",
 		},
+		{
+			expr: "topk(5, a_X)",
+		},
 		// Combinations.
 		{
 			expr: "rate(a_X[1m]) + rate(b_X[1m])",
diff --git a/promql/engine.go b/promql/engine.go
index a93bd4fc9..ad30b1550 100644
--- a/promql/engine.go
+++ b/promql/engine.go
@@ -2507,39 +2507,39 @@ func (ev *evaluator) aggregation(op parser.ItemType, grouping []string, without
 			group.value += delta * (s.V - group.mean)
 
 		case parser.TOPK:
-			if int64(len(group.heap)) < k || group.heap[0].V < s.V || math.IsNaN(group.heap[0].V) {
-				if int64(len(group.heap)) == k {
-					if k == 1 { // For k==1 we can replace in-situ.
-						group.heap[0] = Sample{
-							Point:  Point{V: s.V},
-							Metric: s.Metric,
-						}
-						break
-					}
-					heap.Pop(&group.heap)
-				}
+			// We build a heap of up to k elements, with the smallest element at heap[0].
+			if int64(len(group.heap)) < k {
 				heap.Push(&group.heap, &Sample{
 					Point:  Point{V: s.V},
 					Metric: s.Metric,
 				})
+			} else if group.heap[0].V < s.V || (math.IsNaN(group.heap[0].V) && !math.IsNaN(s.V)) {
+				// This new element is bigger than the previous smallest element - overwrite that.
+				group.heap[0] = Sample{
+					Point:  Point{V: s.V},
+					Metric: s.Metric,
+				}
+				if k > 1 {
+					heap.Fix(&group.heap, 0) // Maintain the heap invariant.
+				}
 			}
 
 		case parser.BOTTOMK:
-			if int64(len(group.reverseHeap)) < k || group.reverseHeap[0].V > s.V || math.IsNaN(group.reverseHeap[0].V) {
-				if int64(len(group.reverseHeap)) == k {
-					if k == 1 { // For k==1 we can replace in-situ.
-						group.reverseHeap[0] = Sample{
-							Point:  Point{V: s.V},
-							Metric: s.Metric,
-						}
-						break
-					}
-					heap.Pop(&group.reverseHeap)
-				}
+			// We build a heap of up to k elements, with the biggest element at heap[0].
+			if int64(len(group.reverseHeap)) < k {
 				heap.Push(&group.reverseHeap, &Sample{
 					Point:  Point{V: s.V},
 					Metric: s.Metric,
 				})
+			} else if group.reverseHeap[0].V > s.V || (math.IsNaN(group.reverseHeap[0].V) && !math.IsNaN(s.V)) {
+				// This new element is smaller than the previous biggest element - overwrite that.
+				group.reverseHeap[0] = Sample{
+					Point:  Point{V: s.V},
+					Metric: s.Metric,
+				}
+				if k > 1 {
+					heap.Fix(&group.reverseHeap, 0) // Maintain the heap invariant.
+				}
 			}
 
 		case parser.QUANTILE: