diff --git a/packages/eslint-plugin/src/rules/unbound-method.ts b/packages/eslint-plugin/src/rules/unbound-method.ts
index 46bbe779c66..b5e8e0cc65b 100644
--- a/packages/eslint-plugin/src/rules/unbound-method.ts
+++ b/packages/eslint-plugin/src/rules/unbound-method.ts
@@ -109,6 +109,9 @@ function isSafeUse(node: TSESTree.Node): boolean {
       return true;
 
     case AST_NODE_TYPES.CallExpression:
+      if (node.type === AST_NODE_TYPES.MemberExpression) {
+        return true;
+      }
       return parent.callee === node;
 
     case AST_NODE_TYPES.ConditionalExpression:
diff --git a/packages/eslint-plugin/tests/rules/unbound-method.test.ts b/packages/eslint-plugin/tests/rules/unbound-method.test.ts
index 520b28fc1d1..59513643c00 100644
--- a/packages/eslint-plugin/tests/rules/unbound-method.test.ts
+++ b/packages/eslint-plugin/tests/rules/unbound-method.test.ts
@@ -15,6 +15,9 @@ const ruleTester = new RuleTester({
 ruleTester.run('unbound-method', rule, {
   valid: [
     `
+new Promise(() => {}).then(console.log)
+    `,
+    `
 class ContainsMethods {
   bound?: () => void;
   unbound?(): void;