diff --git a/CHANGELOG.md b/CHANGELOG.md
index 9b4cb56088..987da7fb6b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -24,6 +24,7 @@ This change log adheres to standards from [Keep a CHANGELOG](http://keepachangel
 - [`namespace`]/`ExportMap`: Fix interface declarations for TypeScript ([#1764], thanks [@julien1619])
 - [`no-unused-modules`]: avoid order-dependence ([#1744], thanks [@darkartur])
 - [`no-internal-modules`]: also check `export from` syntax ([#1691], thanks [@adjerbetian])
+- TypeScript: [`export`]: avoid a crash with `export =` ([#1801], thanks [@ljharb])
 
 ### Changed
 - [Refactor] `no-extraneous-dependencies`: use moduleVisitor ([#1735], thanks [@adamborowski])
@@ -690,6 +691,7 @@ for info on changes for earlier releases.
 [`memo-parser`]: ./memo-parser/README.md
 
 [#1802]: https://github.com/benmosher/eslint-plugin-import/pull/1802
+[#1801]: https://github.com/benmosher/eslint-plugin-import/issues/1801
 [#1788]: https://github.com/benmosher/eslint-plugin-import/pull/1788
 [#1786]: https://github.com/benmosher/eslint-plugin-import/pull/1786
 [#1785]: https://github.com/benmosher/eslint-plugin-import/pull/1785
diff --git a/package.json b/package.json
index da8f028162..3323fa6721 100644
--- a/package.json
+++ b/package.json
@@ -76,7 +76,7 @@
     "eslint-import-test-order-redirect": "file:./tests/files/order-redirect",
     "eslint-module-utils": "file:./utils",
     "eslint-plugin-eslint-plugin": "^2.2.1",
-    "eslint-plugin-import": "2.x",
+    "eslint-plugin-import": "file:./",
     "eslint-plugin-json": "^2.1.1",
     "fs-copy-file-sync": "^1.1.1",
     "glob": "^7.1.6",
diff --git a/src/ExportMap.js b/src/ExportMap.js
index d72952ef4c..dfd9ca155d 100644
--- a/src/ExportMap.js
+++ b/src/ExportMap.js
@@ -590,7 +590,9 @@ ExportMap.parse = function (path, content, context) {
                 moduleBlockNode.declaration :
                 moduleBlockNode
 
-              if (namespaceDecl.type === 'VariableDeclaration') {
+              if (!namespaceDecl) {
+                // TypeScript can check this for us; we needn't
+              } else if (namespaceDecl.type === 'VariableDeclaration') {
                 namespaceDecl.declarations.forEach((d) =>
                   recursivePatternCapture(d.id, (id) => m.namespace.set(
                     id.name,
diff --git a/tests/files/typescript-d-ts/.eslintrc b/tests/files/typescript-d-ts/.eslintrc
new file mode 100644
index 0000000000..f22e9cb620
--- /dev/null
+++ b/tests/files/typescript-d-ts/.eslintrc
@@ -0,0 +1,12 @@
+{
+  "overrides": [
+    {
+      "files": "**.ts",
+      "parser": "@typescript-eslint/parser",
+      "extends": "../../../config/typescript",
+      "rules": {
+        "import/export": "error",
+      },
+    },
+  ],
+}
diff --git a/tests/files/typescript-d-ts/file1.ts b/tests/files/typescript-d-ts/file1.ts
new file mode 100644
index 0000000000..872c30e8af
--- /dev/null
+++ b/tests/files/typescript-d-ts/file1.ts
@@ -0,0 +1,6 @@
+declare namespace ts {
+  const x: string;
+  export { x };
+}
+
+export = ts;
diff --git a/tests/files/typescript-d-ts/file2.ts b/tests/files/typescript-d-ts/file2.ts
new file mode 100644
index 0000000000..e8ed5afca7
--- /dev/null
+++ b/tests/files/typescript-d-ts/file2.ts
@@ -0,0 +1 @@
+export * from './file1.ts'