diff --git a/packages/eslint-plugin/src/rules/no-implied-eval.ts b/packages/eslint-plugin/src/rules/no-implied-eval.ts
index 91bf0d0d319..8e19481653d 100644
--- a/packages/eslint-plugin/src/rules/no-implied-eval.ts
+++ b/packages/eslint-plugin/src/rules/no-implied-eval.ts
@@ -123,6 +123,15 @@ export default util.createRule({
       }
     }
 
+    function isReferenceToGlobalFunction(calleeName: string): boolean {
+      const ref = context
+        .getScope()
+        .references.find(ref => ref.identifier.name === calleeName);
+
+      // ensure it's the "global" version
+      return !ref?.resolved || ref.resolved.defs.length === 0;
+    }
+
     function checkImpliedEval(
       node: TSESTree.NewExpression | TSESTree.CallExpression,
     ): void {
@@ -156,7 +165,11 @@ export default util.createRule({
       }
 
       const [handler] = node.arguments;
-      if (EVAL_LIKE_METHODS.has(calleeName) && !isFunction(handler)) {
+      if (
+        EVAL_LIKE_METHODS.has(calleeName) &&
+        !isFunction(handler) &&
+        isReferenceToGlobalFunction(calleeName)
+      ) {
         context.report({ node: handler, messageId: 'noImpliedEvalError' });
       }
     }
diff --git a/packages/eslint-plugin/tests/rules/no-implied-eval.test.ts b/packages/eslint-plugin/tests/rules/no-implied-eval.test.ts
index c789bd31121..f9c5bd137d6 100644
--- a/packages/eslint-plugin/tests/rules/no-implied-eval.test.ts
+++ b/packages/eslint-plugin/tests/rules/no-implied-eval.test.ts
@@ -276,6 +276,34 @@ class Foo {
   funcw(): void {
     setTimeout(this.a.b.c.bind(this), 1);
   }
+}
+    `,
+    `
+function setTimeout(input: string, value: number) {}
+
+setTimeout('', 0);
+    `,
+    `
+declare module 'my-timers-promises' {
+  export function setTimeout(ms: number): void;
+}
+
+import { setTimeout } from 'my-timers-promises';
+
+setTimeout(1000);
+    `,
+    `
+function setTimeout() {}
+
+{
+  setTimeout(100);
+}
+    `,
+    `
+function setTimeout() {}
+
+{
+  setTimeout("alert('evil!')");
 }
     `,
   ],