diff --git a/packages/playwright-core/src/server/cookieStore.ts b/packages/playwright-core/src/server/cookieStore.ts
index 5d54b6032b789..2d13ecb36ebea 100644
--- a/packages/playwright-core/src/server/cookieStore.ts
+++ b/packages/playwright-core/src/server/cookieStore.ts
@@ -153,6 +153,7 @@ export function parseRawCookie(header: string): RawCookie | null {
     name,
     value,
   };
+  let maxAgeExpires: number | undefined;
   for (let i = 1; i < pairs.length; i++) {
     const [name, value] = pairs[i];
     switch (name.toLowerCase()) {
@@ -167,15 +168,16 @@ export function parseRawCookie(header: string): RawCookie | null {
         }
         break;
       case 'max-age':
-        const maxAgeSec = parseInt(value, 10);
-        if (isFinite(maxAgeSec)) {
-          // From https://datatracker.ietf.org/doc/html/rfc6265#section-5.2.2
+        // From https://datatracker.ietf.org/doc/html/rfc6265#section-5.2.2
+        // If the attribute-value is not an optional "-" followed by digits, ignore the cookie-av.
+        if (/^-?\d+$/.test(value)) {
+          const maxAgeSec = parseInt(value, 10);
           // If delta-seconds is less than or equal to zero (0), let expiry-time
           // be the earliest representable date and time.
           if (maxAgeSec <= 0)
-            cookie.expires = 0;
+            maxAgeExpires = 0;
           else
-            cookie.expires = Math.min(Date.now() / 1000 + maxAgeSec, kMaxCookieExpiresDateInSeconds);
+            maxAgeExpires = Math.min(Date.now() / 1000 + maxAgeSec, kMaxCookieExpiresDateInSeconds);
         }
         break;
       case 'domain':
@@ -207,6 +209,10 @@ export function parseRawCookie(header: string): RawCookie | null {
         break;
     }
   }
+  // https://datatracker.ietf.org/doc/html/rfc6265#section-5.3
+  // Max-Age takes precedence over Expires, regardless of the order of attributes.
+  if (maxAgeExpires !== undefined)
+    cookie.expires = maxAgeExpires;
   return cookie;
 }
 
diff --git a/tests/library/global-fetch-cookie.spec.ts b/tests/library/global-fetch-cookie.spec.ts
index 8503c13784c08..5b54d2485b42d 100644
--- a/tests/library/global-fetch-cookie.spec.ts
+++ b/tests/library/global-fetch-cookie.spec.ts
@@ -313,6 +313,45 @@ it('should remove cookie with negative max-age', async ({ request, server }) =>
   expect(serverRequest.headers.cookie).toBe('c=v');
 });
 
+it('should prefer max-age over expires regardless of the order', async ({ request, server }) => {
+  it.info().annotations.push({ type: 'issue', description: 'https://github.com/microsoft/playwright/issues/43077' });
+
+  const past = 'Thu, 01 Jan 1970 00:00:00 GMT';
+  const future = new Date(Date.now() + 3600_000).toUTCString();
+  server.setRoute('/setcookie.html', (req, res) => {
+    res.setHeader('Set-Cookie', [
+      `a=v; max-age=3600; expires=${past}`,
+      `b=v; expires=${past}; max-age=3600`,
+      `c=v; max-age=-1; expires=${future}`,
+      `d=v; expires=${future}; max-age=-1`,
+    ]);
+    res.end();
+  });
+  await request.get(`${server.PREFIX}/setcookie.html`);
+  const [serverRequest] = await Promise.all([
+    server.waitForRequest('/empty.html'),
+    request.get(server.EMPTY_PAGE)
+  ]);
+  expect(serverRequest.headers.cookie).toBe('a=v; b=v');
+});
+
+it('should ignore max-age that is not a number', async ({ request, server }) => {
+  it.info().annotations.push({ type: 'issue', description: 'https://github.com/microsoft/playwright/issues/43077' });
+
+  server.setRoute('/setcookie.html', (req, res) => {
+    res.setHeader('Set-Cookie', ['a=v; max-age=-1abc', 'b=v; max-age=3600abc', 'c=v; max-age=']);
+    res.end();
+  });
+  await request.get(`${server.PREFIX}/setcookie.html`);
+  const [serverRequest] = await Promise.all([
+    server.waitForRequest('/empty.html'),
+    request.get(server.EMPTY_PAGE)
+  ]);
+  expect(serverRequest.headers.cookie).toBe('a=v; b=v; c=v');
+  const { cookies } = await request.storageState();
+  expect(cookies.map(c => c.expires)).toEqual([-1, -1, -1]);
+});
+
 it('should remove cookie with expires far in the past', async ({ request, server }) => {
   server.setRoute('/setcookie.html', (req, res) => {
     res.setHeader('Set-Cookie', ['a=v; max-age=1000000']);