diff --git a/rules/prefer-add-event-listener.js b/rules/prefer-add-event-listener.js
index 8573bce3e1..1cba8982e6 100644
--- a/rules/prefer-add-event-listener.js
+++ b/rules/prefer-add-event-listener.js
@@ -94,7 +94,7 @@ const create = context => {
 				return;
 			}
 
-			const {left: memberExpression, right: assignedExpression} = node;
+			const {left: memberExpression, right: assignedExpression, operator} = node;
 
 			if (
 				memberExpression.type !== 'MemberExpression'
@@ -132,7 +132,11 @@ const create = context => {
 			} else if (eventTypeName === 'error') {
 				// Disable `onerror` fix, see #1493
 				extra = extraMessages.error;
-			} else {
+			} else if (
+				operator === '='
+				&& node.parent.type === 'ExpressionStatement'
+				&& node.parent.expression === node
+			) {
 				fix = fixer => fixCode(fixer, context.getSourceCode(), node, memberExpression);
 			}
 
diff --git a/test/prefer-add-event-listener.mjs b/test/prefer-add-event-listener.mjs
index 609e86cccc..a28475f211 100644
--- a/test/prefer-add-event-listener.mjs
+++ b/test/prefer-add-event-listener.mjs
@@ -5,7 +5,7 @@ const {test} = getTester(import.meta);
 
 const excludeFooOptions = [{excludedPackages: ['foo']}];
 
-test({
+test.snapshot({
 	valid: [
 		'foo.addEventListener(\'click\', () => {})',
 		'foo.removeEventListener(\'click\', onClick)',
@@ -64,11 +64,6 @@ test({
 			options: excludeFooOptions,
 		},
 	],
-	invalid: [],
-});
-
-test.snapshot({
-	valid: [],
 	invalid: [
 		'foo.onclick = () => {}',
 		'foo.onclick = 1',
@@ -166,6 +161,10 @@ test.snapshot({
 		},
 		'myWorker.port.onmessage = function(e) {}',
 		'((foo)).onclick = ((0, listener))',
+		'window.onload = window.onunload = function() {};',
+		'window.onunload ??= function() {};',
+		'window.onunload ||= function() {};',
+		'window.onunload += function() {};',
 	],
 });
 
diff --git a/test/snapshots/prefer-add-event-listener.mjs.md b/test/snapshots/prefer-add-event-listener.mjs.md
index 09a8e03efd..b3d711f9b2 100644
--- a/test/snapshots/prefer-add-event-listener.mjs.md
+++ b/test/snapshots/prefer-add-event-listener.mjs.md
@@ -441,3 +441,56 @@ Generated by [AVA](https://avajs.dev).
     > 1 | ((foo)).onclick = ((0, listener))␊
         |         ^^^^^^^ Prefer \`addEventListener\` over \`onclick\`.␊
     `
+
+## Invalid #27
+      1 | window.onload = window.onunload = function() {};
+
+> Output
+
+    `␊
+      1 | window.addEventListener('load', window.onunload = function() {});␊
+    `
+
+> Error 1/2
+
+    `␊
+    > 1 | window.onload = window.onunload = function() {};␊
+        |        ^^^^^^ Prefer \`addEventListener\` over \`onload\`.␊
+    `
+
+> Error 2/2
+
+    `␊
+    > 1 | window.onload = window.onunload = function() {};␊
+        |                        ^^^^^^^^ Prefer \`addEventListener\` over \`onunload\`.␊
+    `
+
+## Invalid #28
+      1 | window.onunload ??= function() {};
+
+> Error 1/1
+
+    `␊
+    > 1 | window.onunload ??= function() {};␊
+        |        ^^^^^^^^ Prefer \`addEventListener\` over \`onunload\`.␊
+    `
+
+## Invalid #29
+      1 | window.onunload ||= function() {};
+
+> Error 1/1
+
+    `␊
+    > 1 | window.onunload ||= function() {};␊
+        |        ^^^^^^^^ Prefer \`addEventListener\` over \`onunload\`.␊
+    `
+
+## Invalid #30
+      1 | window.onunload += function() {};
+
+> Error 1/1
+
+    `␊
+    > 1 | window.onunload += function() {};␊
+        |        ^^^^^^^^ Prefer \`addEventListener\` over \`onunload\`.␊
+    `
diff --git a/test/snapshots/prefer-add-event-listener.mjs.snap b/test/snapshots/prefer-add-event-listener.mjs.snap
index 9875badfd3..ddf58857ff 100644
Binary files a/test/snapshots/prefer-add-event-listener.mjs.snap and b/test/snapshots/prefer-add-event-listener.mjs.snap differ