diff --git a/change/react-native-windows-2020-06-12-10-45-34-PR-BackportCallJSQueue.json b/change/react-native-windows-2020-06-12-10-45-34-PR-BackportCallJSQueue.json
new file mode 100644
index 00000000000..52917989b71
--- /dev/null
+++ b/change/react-native-windows-2020-06-12-10-45-34-PR-BackportCallJSQueue.json
@@ -0,0 +1,8 @@
+{
+  "type": "prerelease",
+  "comment": "[0.62] Cherry pick PR #5071 for CallJsFunction queuing",
+  "packageName": "react-native-windows",
+  "email": "vmorozov@microsoft.com",
+  "dependentChangeType": "patch",
+  "date": "2020-06-12T17:45:34.556Z"
+}
diff --git a/vnext/Microsoft.ReactNative/ReactHost/React.h b/vnext/Microsoft.ReactNative/ReactHost/React.h
index 11a44973a68..3ef3ed7b430 100644
--- a/vnext/Microsoft.ReactNative/ReactHost/React.h
+++ b/vnext/Microsoft.ReactNative/ReactHost/React.h
@@ -48,6 +48,7 @@ enum class ReactInstanceState {
   WaitingForDebugger,
   Loaded,
   HasError,
+  Unloaded,
 };
 
 /**An Office wrapper that extends FB's React Instance and makes it a 1:1 relationship with the bundle,
diff --git a/vnext/Microsoft.ReactNative/ReactHost/ReactInstanceWin.cpp b/vnext/Microsoft.ReactNative/ReactHost/ReactInstanceWin.cpp
index 49e4ccf380e..e6b11467f0b 100644
--- a/vnext/Microsoft.ReactNative/ReactHost/ReactInstanceWin.cpp
+++ b/vnext/Microsoft.ReactNative/ReactHost/ReactInstanceWin.cpp
@@ -76,19 +76,13 @@ winrt::Microsoft::ReactNative::IReactPropertyBag ReactContext::Properties() noex
 
 void ReactContext::CallJSFunction(std::string &&module, std::string &&method, folly::dynamic &&params) noexcept {
   if (auto instance = m_reactInstance.GetStrongPtr()) {
-    if (instance->State() == ReactInstanceState::Loaded) {
-      if (auto fbInstance = instance->GetInnerInstance()) {
-        fbInstance->callJSFunction(std::move(module), std::move(method), std::move(params));
-      }
-    }
+    instance->CallJsFunction(std::move(module), std::move(method), std::move(params));
   }
 }
 
 void ReactContext::DispatchEvent(int64_t viewTag, std::string &&eventName, folly::dynamic &&eventData) noexcept {
   if (auto instance = m_reactInstance.GetStrongPtr()) {
-    if (instance->State() == ReactInstanceState::Loaded) {
-      instance->DispatchEvent(viewTag, std::move(eventName), std::move(eventData));
-    }
+    instance->DispatchEvent(viewTag, std::move(eventName), std::move(eventData));
   }
 }
 
@@ -371,6 +365,7 @@ void ReactInstanceWin::LoadJSBundles() noexcept {
           instanceWrapper->loadBundleSync(Mso::Copy(options.Identity));
         } catch (...) {
           strongThis->m_state = ReactInstanceState::HasError;
+          strongThis->AbandonJSCallQueue();
           strongThis->OnReactInstanceLoaded(Mso::ExceptionErrorProvider().MakeErrorCode(std::current_exception()));
           return;
         }
@@ -390,8 +385,10 @@ void ReactInstanceWin::OnReactInstanceLoaded(const Mso::ErrorCode &errorCode) no
           strongThis->m_isLoaded = true;
           if (!errorCode) {
             strongThis->m_state = ReactInstanceState::Loaded;
+            strongThis->DrainJSCallQueue();
           } else {
             strongThis->m_state = ReactInstanceState::HasError;
+            strongThis->AbandonJSCallQueue();
           }
 
           if (auto onLoaded = strongThis->m_options.OnInstanceLoaded.Get()) {
@@ -414,6 +411,8 @@ Mso::Future<void> ReactInstanceWin::Destroy() noexcept {
   }
 
   m_isDestroyed = true;
+  m_state = ReactInstanceState::Unloaded;
+  AbandonJSCallQueue();
 
   if (!m_isLoaded) {
     OnReactInstanceLoaded(Mso::CancellationErrorProvider().MakeErrorCode(true));
@@ -583,6 +582,7 @@ std::function<void(std::string)> ReactInstanceWin::GetErrorCallback() noexcept {
 
 void ReactInstanceWin::OnErrorWithMessage(const std::string &errorMessage) noexcept {
   m_state = ReactInstanceState::HasError;
+  AbandonJSCallQueue();
 
   if (m_redboxHandler && m_redboxHandler->isDevSupportEnabled()) {
     ErrorInfo errorInfo;
@@ -636,12 +636,54 @@ void ReactInstanceWin::OnDebuggerAttach() noexcept {
   m_updateUI();
 }
 
+void ReactInstanceWin::DrainJSCallQueue() noexcept {
+  // Handle all items in the queue one by one.
+  for (;;) {
+    JSCallEntry entry; // To avoid callJSFunction under the lock
+    {
+      std::scoped_lock lock{m_mutex};
+      if (m_state == ReactInstanceState::Loaded && !m_jsCallQueue.empty()) {
+        entry = std::move(m_jsCallQueue.front());
+        m_jsCallQueue.pop_front();
+      } else {
+        break;
+      }
+    }
+
+    if (auto instance = m_instance.LoadWithLock()) {
+      instance->callJSFunction(std::move(entry.ModuleName), std::move(entry.MethodName), std::move(entry.Args));
+    }
+  }
+}
+
+void ReactInstanceWin::AbandonJSCallQueue() noexcept {
+  std::deque<JSCallEntry> jsCallQueue; // To avoid destruction under the lock
+  {
+    std::scoped_lock lock{m_mutex};
+    if (m_state == ReactInstanceState::HasError || m_state == ReactInstanceState::Unloaded) {
+      jsCallQueue = std::move(m_jsCallQueue);
+    }
+  }
+}
+
 void ReactInstanceWin::CallJsFunction(
     std::string &&moduleName,
     std::string &&method,
     folly::dynamic &&params) noexcept {
-  // callJSFunction can be called from any thread. The native bridge will post the call to the right queue internally.
-  if (m_state == ReactInstanceState::Loaded) {
+  bool shouldCall{false}; // To call callJSFunction outside of lock
+  {
+    std::scoped_lock lock{m_mutex};
+    if (m_state == ReactInstanceState::Loaded && m_jsCallQueue.empty()) {
+      shouldCall = true;
+    } else if (
+        m_state == ReactInstanceState::Loading || m_state == ReactInstanceState::WaitingForDebugger ||
+        (m_state == ReactInstanceState::Loaded && !m_jsCallQueue.empty())) {
+      m_jsCallQueue.push_back(JSCallEntry{std::move(moduleName), std::move(method), std::move(params)});
+    }
+    // otherwise ignore the call
+  }
+
+  if (shouldCall) {
     if (auto instance = m_instance.LoadWithLock()) {
       instance->callJSFunction(std::move(moduleName), std::move(method), std::move(params));
     }
@@ -649,11 +691,8 @@ void ReactInstanceWin::CallJsFunction(
 }
 
 void ReactInstanceWin::DispatchEvent(int64_t viewTag, std::string &&eventName, folly::dynamic &&eventData) noexcept {
-  if (m_state == ReactInstanceState::Loaded) {
-    if (auto instance = m_instanceWrapper.LoadWithLock()) {
-      instance->DispatchEvent(viewTag, eventName, std::move(eventData));
-    }
-  }
+  folly::dynamic params = folly::dynamic::array(viewTag, std::move(eventName), std::move(eventData));
+  CallJsFunction("RCTEventEmitter", "receiveEvent", std::move(params));
 }
 
 facebook::react::INativeUIManager *ReactInstanceWin::NativeUIManager() noexcept {
diff --git a/vnext/Microsoft.ReactNative/ReactHost/ReactInstanceWin.h b/vnext/Microsoft.ReactNative/ReactHost/ReactInstanceWin.h
index 5f2957f8389..37d8e4c89de 100644
--- a/vnext/Microsoft.ReactNative/ReactHost/ReactInstanceWin.h
+++ b/vnext/Microsoft.ReactNative/ReactHost/ReactInstanceWin.h
@@ -116,6 +116,15 @@ class ReactInstanceWin final : public Mso::ActiveObject<IReactInstanceInternal,
   friend struct LoadedCallbackGuard;
   void OnReactInstanceLoaded(const Mso::ErrorCode &errorCode) noexcept;
 
+  void DrainJSCallQueue() noexcept;
+  void AbandonJSCallQueue() noexcept;
+
+  struct JSCallEntry {
+    std::string ModuleName;
+    std::string MethodName;
+    folly::dynamic Args;
+  };
+
 #if defined(USE_V8)
   static std::string getApplicationLocalFolder();
 #endif
@@ -162,6 +171,7 @@ class ReactInstanceWin final : public Mso::ActiveObject<IReactInstanceInternal,
   Mso::CntPtr<react::uwp::AppearanceChangeListener> m_appearanceListener;
   std::string m_bundleRootPath;
   Mso::DispatchQueue m_uiQueue;
+  std::deque<JSCallEntry> m_jsCallQueue;
 };
 
 } // namespace Mso::React