diff --git a/ports/openssl/unix/portfile.cmake b/ports/openssl/unix/portfile.cmake
index 98c5dcb549d2be..ca1b864bd974fc 100644
--- a/ports/openssl/unix/portfile.cmake
+++ b/ports/openssl/unix/portfile.cmake
@@ -89,13 +89,19 @@ elseif(VCPKG_TARGET_IS_MINGW)
 elseif(VCPKG_TARGET_IS_EMSCRIPTEN)
     set(OPENSSL_ARCH linux-x32)
     vcpkg_list(APPEND CONFIGURE_OPTIONS
-        threads
         no-engine
         no-asm
         no-sse2
         no-srtp
         --cross-compile-prefix=
     )
+    # Cf. https://emscripten.org/docs/porting/pthreads.html:
+    # For Pthreads support, not just openssl but everything
+    # must be compiled and linked with `-pthread`.
+    # This makes it a triplet/toolchain-wide setting.
+    if(NOT " ${VCPKG_DETECTED_CMAKE_C_FLAGS} " MATCHES " -pthread ")
+        vcpkg_list(APPEND CONFIGURE_OPTIONS no-threads)
+    endif()
 else()
     message(FATAL_ERROR "Unknown platform")
 endif()
diff --git a/ports/openssl/vcpkg.json b/ports/openssl/vcpkg.json
index ef168c96da49a8..55710f889b18c5 100644
--- a/ports/openssl/vcpkg.json
+++ b/ports/openssl/vcpkg.json
@@ -1,7 +1,7 @@
 {
   "name": "openssl",
   "version": "3.4.0",
-  "port-version": 1,
+  "port-version": 2,
   "description": "OpenSSL is an open source project that provides a robust, commercial-grade, and full-featured toolkit for the Transport Layer Security (TLS) and Secure Sockets Layer (SSL) protocols. It is also a general-purpose cryptography library.",
   "homepage": "https://www.openssl.org",
   "license": "Apache-2.0",
diff --git a/versions/baseline.json b/versions/baseline.json
index 7f1de580918eb0..a20deb1cf2b6ac 100644
--- a/versions/baseline.json
+++ b/versions/baseline.json
@@ -6770,7 +6770,7 @@
     },
     "openssl": {
       "baseline": "3.4.0",
-      "port-version": 1
+      "port-version": 2
     },
     "opensubdiv": {
       "baseline": "3.5.0",
diff --git a/versions/o-/openssl.json b/versions/o-/openssl.json
index d4c2408bf7d3c8..8ae2e8c472f9f6 100644
--- a/versions/o-/openssl.json
+++ b/versions/o-/openssl.json
@@ -1,5 +1,10 @@
 {
   "versions": [
+    {
+      "git-tree": "45588fdc81fd5b293cc4729cef3f239d9fb3071c",
+      "version": "3.4.0",
+      "port-version": 2
+    },
     {
       "git-tree": "facccb0b0c47f9804b6e336096d0985c3e541eec",
       "version": "3.4.0",