diff --git a/clang/include/clang/Driver/ToolChain.h b/clang/include/clang/Driver/ToolChain.h
--- a/clang/include/clang/Driver/ToolChain.h
+++ b/clang/include/clang/Driver/ToolChain.h
@@ -711,6 +711,22 @@
       const llvm::fltSemantics *FPType = nullptr) const {
     return llvm::DenormalMode::getIEEE();
   }
+
+  // We want to expand the shortened versions of the triples passed in to
+  // the values used for the bitcode libraries.
+  static llvm::Triple getOpenMPTriple(StringRef TripleStr) {
+    llvm::Triple TT(TripleStr);
+    if (TT.getVendor() == llvm::Triple::UnknownVendor ||
+        TT.getOS() == llvm::Triple::UnknownOS) {
+      if (TT.getArch() == llvm::Triple::nvptx)
+        return llvm::Triple("nvptx-nvidia-cuda");
+      if (TT.getArch() == llvm::Triple::nvptx64)
+        return llvm::Triple("nvptx64-nvidia-cuda");
+      if (TT.getArch() == llvm::Triple::amdgcn)
+        return llvm::Triple("amdgcn-amd-amdhsa");
+    }
+    return TT;
+  }
 };
 
 /// Set a ToolChain's effective triple. Reset it when the registration object
diff --git a/clang/lib/Driver/Driver.cpp b/clang/lib/Driver/Driver.cpp
--- a/clang/lib/Driver/Driver.cpp
+++ b/clang/lib/Driver/Driver.cpp
@@ -792,21 +792,9 @@
       if (HasValidOpenMPRuntime) {
         llvm::StringMap<const char *> FoundNormalizedTriples;
         for (const char *Val : OpenMPTargets->getValues()) {
-          llvm::Triple TT(Val);
+          llvm::Triple TT(ToolChain::getOpenMPTriple(Val));
           std::string NormalizedName = TT.normalize();
 
-          // We want to expand the shortened versions of the triples passed in to
-          // the values used for the bitcode libraries for convenience.
-          if (TT.getVendor() == llvm::Triple::UnknownVendor ||
-              TT.getOS() == llvm::Triple::UnknownOS) {
-            if (TT.getArch() == llvm::Triple::nvptx)
-              TT = llvm::Triple("nvptx-nvidia-cuda");
-            else if (TT.getArch() == llvm::Triple::nvptx64)
-              TT = llvm::Triple("nvptx64-nvidia-cuda");
-            else if (TT.getArch() == llvm::Triple::amdgcn)
-              TT = llvm::Triple("amdgcn-amd-amdhsa");
-          }
-
           // Make sure we don't have a duplicate triple.
           auto Duplicate = FoundNormalizedTriples.find(NormalizedName);
           if (Duplicate != FoundNormalizedTriples.end()) {
diff --git a/clang/lib/Driver/ToolChain.cpp b/clang/lib/Driver/ToolChain.cpp
--- a/clang/lib/Driver/ToolChain.cpp
+++ b/clang/lib/Driver/ToolChain.cpp
@@ -1129,8 +1129,10 @@
         A->getOption().matches(options::OPT_Xopenmp_target);
 
     if (A->getOption().matches(options::OPT_Xopenmp_target_EQ)) {
+      llvm::Triple TT(getOpenMPTriple(A->getValue(0)));
+
       // Passing device args: -Xopenmp-target=<triple> -opt=val.
-      if (A->getValue(0) == getTripleString())
+      if (TT.getTriple() == getTripleString())
         Index = Args.getBaseArgs().MakeIndex(A->getValue(1));
       else
         continue;
diff --git a/clang/test/Driver/openmp-offload-gpu.c b/clang/test/Driver/openmp-offload-gpu.c
--- a/clang/test/Driver/openmp-offload-gpu.c
+++ b/clang/test/Driver/openmp-offload-gpu.c
@@ -343,3 +343,10 @@
 // RUN:   | FileCheck -check-prefix=SAVE_TEMPS_NAMES %s
 
 // SAVE_TEMPS_NAMES-NOT: "GNU::Linker"{{.*}}["[[SAVE_TEMPS_INPUT1:.*\.o]]", "[[SAVE_TEMPS_INPUT1]]"]
+
+// RUN:   %clang -### -fopenmp=libomp -fopenmp-targets=nvptx64 -Xopenmp-target=nvptx64 -march=sm_35 \
+// RUN:          -save-temps -no-canonical-prefixes %s -o openmp-offload-gpu 2>&1 \
+// RUN:   | FileCheck -check-prefix=TRIPLE %s
+
+// TRIPLE: "-triple" "nvptx64-nvidia-cuda"
+// TRIPLE: "-target-cpu" "sm_35"