diff --git a/packages/babel-parser/src/plugins/typescript/index.js b/packages/babel-parser/src/plugins/typescript/index.js
index c4ab4f780b38..a205518396f5 100644
--- a/packages/babel-parser/src/plugins/typescript/index.js
+++ b/packages/babel-parser/src/plugins/typescript/index.js
@@ -1469,35 +1469,6 @@ export default (superClass: Class<Parser>): Class<Parser> =>
       );
     }
 
-    tsTryParseTypeArguments(): ?N.TsTypeParameterInstantiation {
-      if (!this.isRelational("<")) {
-        return undefined;
-      }
-      const state = this.state.clone();
-      const node = this.startNode();
-      const params = this.tsInType(() =>
-        // Temporarily remove a JSX parsing context, which makes us scan different tokens.
-        this.tsInNoContext(() => {
-          this.next();
-          return this.tsTryParseDelimitedList(
-            "TypeParametersOrArguments",
-            this.tsParseType.bind(this),
-          );
-        }),
-      );
-      if (params) {
-        node.params = params;
-        // This reads the next token after the `>` too, so do this in the enclosing context.
-        // But be sure not to parse a regex in the jsx expression `<C<number> />`, so set exprAllowed = false
-        this.state.exprAllowed = false;
-        if (this.eatRelational(">")) {
-          return this.finishNode(node, "TSTypeParameterInstantiation");
-        }
-      }
-      this.state = state;
-      return undefined;
-    }
-
     tsParseTypeArguments(): N.TsTypeParameterInstantiation {
       const node = this.startNode();
       node.params = this.tsInType(() =>
@@ -1656,28 +1627,27 @@ export default (superClass: Class<Parser>): Class<Parser> =>
           const node: N.CallExpression = this.startNodeAt(startPos, startLoc);
           node.callee = base;
 
-          const typeArguments = this.tsTryParseTypeArguments();
-          if (!typeArguments) {
-            return undefined;
-          }
-
-          if (!noCalls && this.eat(tt.parenL)) {
-            // possibleAsync always false here, because we would have handled it above.
-            // $FlowIgnore (won't be any undefined arguments)
-            node.arguments = this.parseCallExpressionArguments(
-              tt.parenR,
-              /* possibleAsync */ false,
-            );
-            node.typeParameters = typeArguments;
-            return this.finishCallExpression(node);
-          } else if (this.match(tt.backQuote)) {
-            return this.parseTaggedTemplateExpression(
-              startPos,
-              startLoc,
-              base,
-              state,
-              typeArguments,
-            );
+          const typeArguments = this.tsParseTypeArguments();
+
+          if (typeArguments) {
+            if (!noCalls && this.eat(tt.parenL)) {
+              // possibleAsync always false here, because we would have handled it above.
+              // $FlowIgnore (won't be any undefined arguments)
+              node.arguments = this.parseCallExpressionArguments(
+                tt.parenR,
+                /* possibleAsync */ false,
+              );
+              node.typeParameters = typeArguments;
+              return this.finishCallExpression(node);
+            } else if (this.match(tt.backQuote)) {
+              return this.parseTaggedTemplateExpression(
+                startPos,
+                startLoc,
+                base,
+                state,
+                typeArguments,
+              );
+            }
           }
 
           this.unexpected();
@@ -2473,8 +2443,12 @@ export default (superClass: Class<Parser>): Class<Parser> =>
     jsxParseOpeningElementAfterName(
       node: N.JSXOpeningElement,
     ): N.JSXOpeningElement {
-      const typeArguments = this.tsTryParseTypeArguments();
-      if (typeArguments) node.typeParameters = typeArguments;
+      if (this.isRelational("<")) {
+        const typeArguments = this.tsTryParseAndCatch(() =>
+          this.tsParseTypeArguments(),
+        );
+        if (typeArguments) node.typeParameters = typeArguments;
+      }
       return super.jsxParseOpeningElementAfterName(node);
     }