Updated 5:58 p.m. ET

Yum Brands (YUM) owes its existence to American fast food, but it needs China's hunger for KFC, Taco Bell and Pizza Hut to balance its books. And China seems more than happy to oblige.

The cheap-eats giant said profit rose by 19% in the quarter, propelled by gains in China. Customers there increased their appetites for late-night nachos and buckets of Extra Crispy in the third quarter, a nice break for Yum after its adjusted operating profit in China fell 4% in spring.

Yum reported a profit of $471 million, or $1 per share, up from from $383 million, or 80 cents per share, a year earlier. Excluding one-time gains related to refranchising and acquisitions, earnings came in at 99 cents compared with 83 cents a year earlier. Revenue rose 9% to $3.57 billion. Analysts polled by FactSet expected a profit of 97 cents per share on revenue of $3.66 billion. That's 2 cents lower than what they had pegged in May, but that spring shakeup in China made investors more than a little nervous.

Shares of Yum rose nearly 4% in after-hours trading. The stock closed Tuesday down more than 1% to $66.04.

Yum, based in Louisville, Ky., has 38,000 restaurants in 120 countries, including more than 16,000 in the U.S. However, just 12% of those U.S. stores -- little more than 1,900 -- are company-owned. Compare that with China, where more than 3,700 (83%) of that country's 4,465 stores are owned by Yum itself and where the impact on Yum's bottom line is nearly double that of the U.S. market.

China's tastes for KFC and Pizza Hut are an indicator of just how affordable simple luxuries like fast food are to the Chinese middle class amid rising wages. If Chinese workers are gorging themselves on thick crust despite the increased cost of opening a Pizza Hut in their neighborhood, it bodes well for the Chinese economy in general.

A sound Chinese economy is especially important to Yum as some of its other overseas markets soften. Yum has been largely shielded from European instability because most of its Europe locations are in Great Britain, France and Germany, but it still has stores in other, less-stable economies. Seeking Alpha analyst Markos Kaminis warns that residual anti-American sentiment from Arab Spring protests and unrest in Yum markets including Egypt (171 stores in 2011), Malaysia (795), Indonesia (661), Thailand (492), Saudi Arabia (321) and the United Arab Emirates (153) could take a toll on Yum's business as well.

The strong third quarter in China may go a long way toward returning Yum to its early 2012 form, when it outperformed McDonald's (MCD) stock by 30%. Yum has fallen behind the Golden Arches by more than 8% since but has predicted a return to double-digit profit growth in China for the second half of the year.

That turned out to be the case in its third quarter. Operating profit in China rose by 22%, adjusting for currency fluctuations, the company reported. That's one impressive food run, but it's an order Yum will gladly take.