diff --git a/src/network/ssl/qsslkey_openssl.cpp b/src/network/ssl/qsslkey_openssl.cpp
index 79df33eccab..26119023d14 100644
--- a/src/network/ssl/qsslkey_openssl.cpp
+++ b/src/network/ssl/qsslkey_openssl.cpp
@@ -84,6 +84,9 @@ void QSslKeyPrivate::clear(bool deep)
 
 bool QSslKeyPrivate::fromEVP_PKEY(EVP_PKEY *pkey)
 {
+    if (pkey == nullptr)
+        return false;
+
     if (pkey->type == EVP_PKEY_RSA) {
         isNull = false;
         algorithm = QSsl::Rsa;
diff --git a/src/network/ssl/qsslsocket_openssl.cpp b/src/network/ssl/qsslsocket_openssl.cpp
index 644dfdb6a89..ab82cdcfc9a 100644
--- a/src/network/ssl/qsslsocket_openssl.cpp
+++ b/src/network/ssl/qsslsocket_openssl.cpp
@@ -1805,7 +1805,7 @@ bool QSslSocketBackendPrivate::importPkcs12(QIODevice *device,
     }
 
     // Extract the data
-    EVP_PKEY *pkey;
+    EVP_PKEY *pkey = nullptr;
     X509 *x509;
     STACK_OF(X509) *ca = 0;
 
diff --git a/tests/auto/network/ssl/qsslcertificate/pkcs12/README b/tests/auto/network/ssl/qsslcertificate/pkcs12/README
index 1828d089c1c..231567f5863 100644
--- a/tests/auto/network/ssl/qsslcertificate/pkcs12/README
+++ b/tests/auto/network/ssl/qsslcertificate/pkcs12/README
@@ -1,8 +1,19 @@
-The PKCS#12 bundle was created by running the following on
-in the qsslsocket/certs directory:
+The PKCS#12 bundle was created by running the following in an
+interactive shell in ../../qsslsocket/certs/:
 
-openssl pkcs12 -export -in leaf.crt -inkey leaf.key \
-               -out leaf.p12 \
+openssl pkcs12 -export -in leaf.crt \
+               -inkey leaf.key -out leaf.p12 \
                -certfile inter.crt -CAfile ca.crt
 
-No password was provided.
+An empty password was provided (twice).  The pkcs.crt and pkcs.key
+files were then copied here and leaf.p12 was moved here.
+
+
+The test-case with no private key (in a valid PKCS12 file) was created
+similarly but with the command adjusted to:
+
+openssl pkcs12 -export -in leaf.crt \
+               -nokeys -out leaf-nokey.p12 \
+               -certfile inter.crt -CAfile ca.crt
+
+The file leaf-nokey.p12 was then moved here.
diff --git a/tests/auto/network/ssl/qsslcertificate/pkcs12/leaf-nokey.p12 b/tests/auto/network/ssl/qsslcertificate/pkcs12/leaf-nokey.p12
new file mode 100644
index 00000000000..032bf97b1b5
Binary files /dev/null and b/tests/auto/network/ssl/qsslcertificate/pkcs12/leaf-nokey.p12 differ
diff --git a/tests/auto/network/ssl/qsslcertificate/tst_qsslcertificate.cpp b/tests/auto/network/ssl/qsslcertificate/tst_qsslcertificate.cpp
index fced638ecb5..064efc120bd 100644
--- a/tests/auto/network/ssl/qsslcertificate/tst_qsslcertificate.cpp
+++ b/tests/auto/network/ssl/qsslcertificate/tst_qsslcertificate.cpp
@@ -1308,6 +1308,7 @@ void tst_QSslCertificate::version()
 
 void tst_QSslCertificate::pkcs12()
 {
+    // See pkcs12/README for how to generate the PKCS12 files used here.
     if (!QSslSocket::supportsSsl()) {
         qWarning("SSL not supported, skipping test");
         return;
@@ -1349,6 +1350,15 @@ void tst_QSslCertificate::pkcs12()
     QVERIFY(!caCerts.isEmpty());
     QCOMPARE(caCerts.first(), caCert.first());
     QCOMPARE(caCerts, caCert);
+
+    // QTBUG-62335 - Fail (found no private key) but don't crash:
+    QFile nocert(testDataDir + QLatin1String("/pkcs12/leaf-nokey.p12"));
+    ok = nocert.open(QIODevice::ReadOnly);
+    QVERIFY(ok);
+    QTest::ignoreMessage(QtWarningMsg, "Unable to convert private key");
+    ok = QSslCertificate::importPkcs12(&nocert, &key, &cert, &caCerts);
+    QVERIFY(!ok);
+    nocert.close();
 }
 
 #endif // QT_NO_SSL