diff --git a/test/e2e/framework/pod/node_selection.go b/test/e2e/framework/pod/node_selection.go
index 9931afa6566..01d1d4c165c 100644
--- a/test/e2e/framework/pod/node_selection.go
+++ b/test/e2e/framework/pod/node_selection.go
@@ -79,3 +79,11 @@ func SetAffinity(nodeSelection *NodeSelection, nodeName string) {
 func SetAntiAffinity(nodeSelection *NodeSelection, nodeName string) {
 	setNodeAffinityRequirement(nodeSelection, v1.NodeSelectorOpNotIn, nodeName)
 }
+
+// SetNodeAffinity modifies the given pod object with
+// NodeAffinity to the given node name.
+func SetNodeAffinity(pod *v1.Pod, nodeName string) {
+	nodeSelection := &NodeSelection{}
+	SetAffinity(nodeSelection, nodeName)
+	pod.Spec.Affinity = nodeSelection.Affinity
+}
diff --git a/test/e2e/storage/utils/host_exec.go b/test/e2e/storage/utils/host_exec.go
index 395065b43e1..7f5077888e3 100644
--- a/test/e2e/storage/utils/host_exec.go
+++ b/test/e2e/storage/utils/host_exec.go
@@ -73,9 +73,14 @@ func (h *hostExecutor) launchNodeExecPod(node string) *v1.Pod {
 	f := h.Framework
 	cs := f.ClientSet
 	ns := f.Namespace
+
 	hostExecPod := e2epod.NewExecPodSpec(ns.Name, "", true)
 	hostExecPod.GenerateName = fmt.Sprintf("hostexec-%s-", node)
-	hostExecPod.Spec.NodeName = node
+	// Use NodeAffinity instead of NodeName so that pods will not
+	// be immediately Failed by kubelet if it's out of space. Instead
+	// Pods will be pending in the scheduler until there is space freed
+	// up.
+	e2epod.SetNodeAffinity(hostExecPod, node)
 	hostExecPod.Spec.Volumes = []v1.Volume{
 		{
 			// Required to enter into host mount namespace via nsenter.