diff --git a/util/testutil/port.go b/util/testutil/port.go
index 1e449b123..7cf4cf1cc 100644
--- a/util/testutil/port.go
+++ b/util/testutil/port.go
@@ -15,21 +15,56 @@ package testutil
 
 import (
 	"net"
+	"sync"
 	"testing"
 )
 
+var (
+	mu        sync.Mutex
+	usedPorts []int
+)
+
 // RandomUnprivilegedPort returns valid unprivileged random port number which can be used for testing.
 func RandomUnprivilegedPort(t *testing.T) int {
 	t.Helper()
+	mu.Lock()
+	defer mu.Unlock()
+
+	port, err := getPort()
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	for portWasUsed(port) {
+		port, err = getPort()
+		if err != nil {
+			t.Fatal(err)
+		}
+	}
+
+	usedPorts = append(usedPorts, port)
+
+	return port
+}
+
+func portWasUsed(port int) bool {
+	for _, usedPort := range usedPorts {
+		if port == usedPort {
+			return true
+		}
+	}
+	return false
+}
 
+func getPort() (int, error) {
 	listener, err := net.Listen("tcp", ":0")
 	if err != nil {
-		t.Fatalf("Listening on random port: %v", err)
+		return 0, err
 	}
 
 	if err := listener.Close(); err != nil {
-		t.Fatalf("Closing listener: %v", err)
+		return 0, err
 	}
 
-	return listener.Addr().(*net.TCPAddr).Port
+	return listener.Addr().(*net.TCPAddr).Port, nil
 }