diff --git a/lib/dispatcher/client-h2.js b/lib/dispatcher/client-h2.js
index 18082a8b80b..31552cee7ef 100644
--- a/lib/dispatcher/client-h2.js
+++ b/lib/dispatcher/client-h2.js
@@ -152,6 +152,21 @@ function requeueUnsentRequest (client, request) {
   client[kQueue].splice(client[kPendingIdx] + 1, 0, request)
 }
 
+function completeRequest (client, request, resetPendingIdx = false) {
+  const index = client[kQueue].indexOf(request, client[kRunningIdx])
+
+  if (index === -1 || index >= client[kPendingIdx]) {
+    return
+  }
+
+  client[kQueue].splice(index, 1)
+  client[kPendingIdx]--
+
+  if (resetPendingIdx && client[kPendingIdx] < client[kRunningIdx]) {
+    client[kPendingIdx] = client[kRunningIdx]
+  }
+}
+
 function canRetryRequestAfterGoAway (request) {
   const { body } = request
 
@@ -479,7 +494,9 @@ function onHttp2SessionClose () {
     const requests = client[kQueue].splice(client[kRunningIdx])
     for (let i = 0; i < requests.length; i++) {
       const request = requests[i]
-      util.errorRequest(client, request, err)
+      if (request != null) {
+        util.errorRequest(client, request, err)
+      }
     }
   }
 }
@@ -742,11 +759,7 @@ function writeH2 (client, request) {
     }
 
     requestFinalized = true
-    client[kQueue][client[kRunningIdx]++] = null
-
-    if (resetPendingIdx && client[kPendingIdx] < client[kRunningIdx]) {
-      client[kPendingIdx] = client[kRunningIdx]
-    }
+    completeRequest(client, request, resetPendingIdx)
 
     client[kResume]()
   }
diff --git a/lib/dispatcher/client.js b/lib/dispatcher/client.js
index 37d3d139825..8a4f65171bd 100644
--- a/lib/dispatcher/client.js
+++ b/lib/dispatcher/client.js
@@ -395,7 +395,9 @@ class Client extends DispatcherBase {
       const requests = this[kQueue].splice(this[kPendingIdx])
       for (let i = 0; i < requests.length; i++) {
         const request = requests[i]
-        util.errorRequest(this, request, err)
+        if (request != null) {
+          util.errorRequest(this, request, err)
+        }
       }
 
       const callback = () => {
@@ -434,7 +436,9 @@ function onError (client, err) {
 
     for (let i = 0; i < requests.length; i++) {
       const request = requests[i]
-      util.errorRequest(client, request, err)
+      if (request != null) {
+        util.errorRequest(client, request, err)
+      }
     }
     assert(client[kSize] === 0)
   }
diff --git a/test/issue-5404.js b/test/issue-5404.js
new file mode 100644
index 00000000000..b293420ebe4
--- /dev/null
+++ b/test/issue-5404.js
@@ -0,0 +1,69 @@
+'use strict'
+
+const { test } = require('node:test')
+const assert = require('node:assert')
+const { once } = require('node:events')
+const { createServer } = require('node:http2')
+
+const { Client } = require('..')
+const { kQueue } = require('../lib/core/symbols')
+
+// Regression test for https://github.com/nodejs/undici/issues/5404.
+// HTTP/2 streams can complete out of order. Completing the second stream first
+// must not clear the first request's queue slot; otherwise destroying the
+// client can lose or mis-error the still-running request.
+test('h2: out-of-order completion preserves running requests during destroy', async () => {
+  const server = createServer()
+  let firstStream
+
+  server.on('sessionError', () => {})
+  server.on('stream', (stream, headers) => {
+    switch (headers[':path']) {
+      case '/first':
+        firstStream = stream
+        break
+      case '/second':
+        stream.respond({ ':status': 200 })
+        stream.end('second')
+        break
+      case '/third':
+        stream.respond({ ':status': 200 })
+        stream.end('third')
+        break
+      default:
+        stream.respond({ ':status': 404 })
+        stream.end()
+    }
+  })
+
+  await once(server.listen(0), 'listening')
+
+  const client = new Client(`http://localhost:${server.address().port}`, {
+    allowH2: true,
+    useH2c: true,
+    maxConcurrentStreams: 2
+  })
+
+  try {
+    const first = client.request({ path: '/first', method: 'GET' })
+    const firstError = first.then(
+      () => null,
+      err => err
+    )
+
+    const second = await client.request({ path: '/second', method: 'GET' })
+    assert.strictEqual(await second.body.text(), 'second')
+
+    const third = await client.request({ path: '/third', method: 'GET' })
+    assert.strictEqual(await third.body.text(), 'third')
+
+    assert.strictEqual(firstStream.destroyed, false)
+    assert.deepStrictEqual(client[kQueue].map(request => request?.path), ['/first'])
+
+    await client.destroy(new Error('boom'))
+    assert.strictEqual((await firstError).message, 'boom')
+  } finally {
+    await client.destroy().catch(() => {})
+    server.close()
+  }
+})