diff -Nuar a/vendor/magento/module-sales/Model/Order/Invoice/Total/Discount.php b/vendor/magento/module-sales/Model/Order/Invoice/Total/Discount.php
index acd0d0c67d8..ef7205b3744 100644
--- a/vendor/magento/module-sales/Model/Order/Invoice/Total/Discount.php
+++ b/vendor/magento/module-sales/Model/Order/Invoice/Total/Discount.php
@@ -5,13 +5,20 @@
  */
 namespace Magento\Sales\Model\Order\Invoice\Total;
 
+use Magento\Sales\Model\Order\Invoice;
+
+/**
+ * Discount invoice
+ */
 class Discount extends AbstractTotal
 {
     /**
-     * @param \Magento\Sales\Model\Order\Invoice $invoice
+     * Collect invoice
+     *
+     * @param Invoice $invoice
      * @return $this
      */
-    public function collect(\Magento\Sales\Model\Order\Invoice $invoice)
+    public function collect(Invoice $invoice)
     {
         $invoice->setDiscountAmount(0);
         $invoice->setBaseDiscountAmount(0);
@@ -24,14 +31,7 @@ class Discount extends AbstractTotal
          * So basically if we have invoice with positive discount and it
          * was not canceled we don't add shipping discount to this one.
          */
-        $addShippingDiscount = true;
-        foreach ($invoice->getOrder()->getInvoiceCollection() as $previousInvoice) {
-            if ($previousInvoice->getDiscountAmount()) {
-                $addShippingDiscount = false;
-            }
-        }
-
-        if ($addShippingDiscount) {
+        if ($this->isShippingDiscount($invoice)) {
             $totalDiscountAmount = $totalDiscountAmount + $invoice->getOrder()->getShippingDiscountAmount();
             $baseTotalDiscountAmount = $baseTotalDiscountAmount +
                 $invoice->getOrder()->getBaseShippingDiscountAmount();
@@ -71,8 +71,29 @@ class Discount extends AbstractTotal
         $invoice->setDiscountAmount(-$totalDiscountAmount);
         $invoice->setBaseDiscountAmount(-$baseTotalDiscountAmount);
 
-        $invoice->setGrandTotal($invoice->getGrandTotal() - $totalDiscountAmount);
-        $invoice->setBaseGrandTotal($invoice->getBaseGrandTotal() - $baseTotalDiscountAmount);
+        $grandTotal = $invoice->getGrandTotal() - $totalDiscountAmount < 0.0001
+            ? 0 : $invoice->getGrandTotal() - $totalDiscountAmount;
+        $baseGrandTotal = $invoice->getBaseGrandTotal() - $baseTotalDiscountAmount < 0.0001
+            ? 0 : $invoice->getBaseGrandTotal() - $baseTotalDiscountAmount;
+        $invoice->setGrandTotal($grandTotal);
+        $invoice->setBaseGrandTotal($baseGrandTotal);
         return $this;
     }
+
+    /**
+     * Checking if shipping discount was added in previous invoices.
+     *
+     * @param Invoice $invoice
+     * @return bool
+     */
+    private function isShippingDiscount(Invoice $invoice): bool
+    {
+        $addShippingDiscount = true;
+        foreach ($invoice->getOrder()->getInvoiceCollection() as $previousInvoice) {
+            if ($previousInvoice->getDiscountAmount()) {
+                $addShippingDiscount = false;
+            }
+        }
+        return $addShippingDiscount;
+    }
 }
diff -Nuar a/vendor/magento/module-sales/Model/ResourceModel/Order/Handler/State.php b/vendor/magento/module-sales/Model/ResourceModel/Order/Handler/State.php
index de15a627583..47395b17afe 100644
--- a/vendor/magento/module-sales/Model/ResourceModel/Order/Handler/State.php
+++ b/vendor/magento/module-sales/Model/ResourceModel/Order/Handler/State.php
@@ -9,7 +9,7 @@ namespace Magento\Sales\Model\ResourceModel\Order\Handler;
 use Magento\Sales\Model\Order;
 
 /**
- * Class State
+ * Checking order status and adjusting order status before saving
  */
 class State
 {
@@ -34,6 +34,7 @@ class State
             if (in_array($currentState, [Order::STATE_PROCESSING, Order::STATE_COMPLETE])
                 && !$order->canCreditmemo()
                 && !$order->canShip()
+                && $order->getIsNotVirtual()
             ) {
                 $order->setState(Order::STATE_CLOSED)
                     ->setStatus($order->getConfig()->getStateDefaultStatus(Order::STATE_CLOSED));