diff --git a/lib/internal/fs/promises.js b/lib/internal/fs/promises.js
index 41c17de95ed..6f5d2921a59 100644
--- a/lib/internal/fs/promises.js
+++ b/lib/internal/fs/promises.js
@@ -100,6 +100,7 @@ const kRefs = Symbol('kRefs');
 const kClosePromise = Symbol('kClosePromise');
 const kCloseResolve = Symbol('kCloseResolve');
 const kCloseReject = Symbol('kCloseReject');
+const kClosing = Symbol('kClosing');
 const kRef = Symbol('kRef');
 const kUnref = Symbol('kUnref');
 const kLocked = Symbol('kLocked');
@@ -137,7 +138,17 @@ class FileHandle extends EventEmitterMixin(JSTransferable) {
     this[kFd] = filehandle ? filehandle.fd : -1;
 
     this[kRefs] = 1;
-    this[kClosePromise] = null;
+    this[kClosing] = false;
+    this[kClosePromise] = SafePromisePrototypeFinally(
+      new Promise((resolve, reject) => {
+        this[kCloseResolve] = resolve;
+        this[kCloseReject] = reject;
+      }), () => {
+        this[kClosePromise] = undefined;
+        this[kCloseReject] = undefined;
+        this[kCloseResolve] = undefined;
+      },
+    );
   }
 
   getAsyncId() {
@@ -216,31 +227,21 @@ class FileHandle extends EventEmitterMixin(JSTransferable) {
       return PromiseResolve();
     }
 
-    if (this[kClosePromise]) {
+    if (this[kClosing]) {
       return this[kClosePromise];
     }
 
-    this[kRefs]--;
-    if (this[kRefs] === 0) {
-      this[kFd] = -1;
-      this[kClosePromise] = SafePromisePrototypeFinally(
-        this[kHandle].close(),
-        () => { this[kClosePromise] = undefined; },
-      );
-    } else {
-      this[kClosePromise] = SafePromisePrototypeFinally(
-        new Promise((resolve, reject) => {
-          this[kCloseResolve] = resolve;
-          this[kCloseReject] = reject;
-        }), () => {
-          this[kClosePromise] = undefined;
-          this[kCloseReject] = undefined;
-          this[kCloseResolve] = undefined;
-        },
-      );
-    }
+    this[kClosing] = true;
+    this[kUnref]();
+
+    SafePromisePrototypeFinally(
+      this[kClosePromise],
+      () => {
+        this[kClosePromise] = undefined;
+        this.emit('close');
+      }
+    );
 
-    this.emit('close');
     return this[kClosePromise];
   };
 
@@ -252,7 +253,7 @@ class FileHandle extends EventEmitterMixin(JSTransferable) {
   readableWebStream() {
     if (this[kFd] === -1)
       throw new ERR_INVALID_STATE('The FileHandle is closed');
-    if (this[kClosePromise])
+    if (this[kClosing])
       throw new ERR_INVALID_STATE('The FileHandle is closing');
     if (this[kLocked])
       throw new ERR_INVALID_STATE('The FileHandle is locked');
@@ -311,7 +312,7 @@ class FileHandle extends EventEmitterMixin(JSTransferable) {
   }
 
   [kTransfer]() {
-    if (this[kClosePromise] || this[kRefs] > 1) {
+    if (this[kClosing] || this[kRefs] > 1) {
       throw lazyDOMException('Cannot transfer FileHandle while in use',
                              'DataCloneError');
     }
@@ -337,11 +338,14 @@ class FileHandle extends EventEmitterMixin(JSTransferable) {
   }
 
   [kRef]() {
+    assert(this[kFd] !== -1);
     this[kRefs]++;
   }
 
   [kUnref]() {
+    assert(this[kFd] !== -1);
     this[kRefs]--;
+
     if (this[kRefs] === 0) {
       this[kFd] = -1;
       PromisePrototypeThen(
@@ -980,6 +984,7 @@ module.exports = {
   },
 
   FileHandle,
+  kRefs,
   kRef,
   kUnref,
 };
diff --git a/lib/internal/fs/streams.js b/lib/internal/fs/streams.js
index f75d0fba917..a5c300049fd 100644
--- a/lib/internal/fs/streams.js
+++ b/lib/internal/fs/streams.js
@@ -26,7 +26,7 @@ const {
 } = require('internal/validators');
 const { errorOrDestroy } = require('internal/streams/destroy');
 const fs = require('fs');
-const { kRef, kUnref, FileHandle } = require('internal/fs/promises');
+const { kRef, kUnref, kRefs, FileHandle } = require('internal/fs/promises');
 const { Buffer } = require('buffer');
 const {
   copyObject,
@@ -36,6 +36,8 @@ const {
 } = require('internal/fs/utils');
 const { Readable, Writable, finished } = require('stream');
 const { toPathIfFileURL } = require('internal/url');
+const assert = require('internal/assert');
+
 const kIoDone = Symbol('kIoDone');
 const kIsPerformingIO = Symbol('kIsPerformingIO');
 
@@ -80,15 +82,21 @@ function _construct(callback) {
 }
 
 // This generates an fs operations structure for a FileHandle
-const FileHandleOperations = (handle) => {
+const FileHandleOperations = (handle, closeHandler) => {
   return {
     open: (path, flags, mode, cb) => {
       throw new ERR_METHOD_NOT_IMPLEMENTED('open()');
     },
     close: (fd, cb) => {
+      handle.off('close', closeHandler);
       handle[kUnref]();
-      PromisePrototypeThen(handle.close(),
-                           () => cb(), cb);
+      if (handle[kRefs] > 1) {
+        // Someone else has a ref to the handle.
+        process.nextTick(cb);
+      } else {
+        PromisePrototypeThen(handle.close(),
+                             () => cb(), cb);
+      }
     },
     read: (fd, buf, offset, length, pos, cb) => {
       PromisePrototypeThen(handle.read(buf, offset, length, pos),
@@ -134,10 +142,12 @@ function importFd(stream, options) {
       // FileHandle is not supported with custom fs operations
       throw new ERR_METHOD_NOT_IMPLEMENTED('FileHandle with fs');
     }
+    assert(options.fd[kRefs] > 0);
+    const closeHandler = FunctionPrototypeBind(stream.close, stream);
     stream[kHandle] = options.fd;
-    stream[kFs] = FileHandleOperations(stream[kHandle]);
+    stream[kFs] = FileHandleOperations(stream[kHandle], closeHandler);
     stream[kHandle][kRef]();
-    options.fd.on('close', FunctionPrototypeBind(stream.close, stream));
+    stream[kHandle].on('close', closeHandler);
     return options.fd.fd;
   }
 
diff --git a/test/parallel/test-fs-read-stream-file-handle.js b/test/parallel/test-fs-read-stream-file-handle.js
index 810745149dc..2560b7e07f7 100644
--- a/test/parallel/test-fs-read-stream-file-handle.js
+++ b/test/parallel/test-fs-read-stream-file-handle.js
@@ -29,12 +29,22 @@ fs.promises.open(file, 'r').then((handle) => {
 fs.promises.open(file, 'r').then((handle) => {
   handle.on('close', common.mustCall());
   const stream = fs.createReadStream(null, { fd: handle });
-  stream.on('data', common.mustNotCall());
+  stream.on('data', common.mustCall(() => {
+    stream.destroy();
+  }));
   stream.on('close', common.mustCall());
 
   return handle.close();
 }).then(common.mustCall());
 
+fs.promises.open(file, 'r').then((handle) => {
+  handle.on('close', common.mustCall());
+  const stream = fs.createReadStream(null, { fd: handle });
+  stream.on('data', common.mustNotCall());
+  stream.on('close', common.mustCall());
+  stream.destroy();
+}).then(common.mustCall());
+
 fs.promises.open(file, 'r').then((handle) => {
   handle.on('close', common.mustCall());
   const stream = fs.createReadStream(null, { fd: handle });