Mexico's peso suffers biggest tumble in 2 months

* Mexico peso sinks by most since Oct. 1

* Blows past key 12.80 level as long bets are unwound

* IPC stock index sheds more than 1 pct (Recasts; adds comments and closing stock prices)

MEXICO CITY, Dec 8 (Reuters) - Mexico's peso sank by the most in more than two months on Tuesday as worries over Dubai's debt troubles and a downgrade of Greece stoked concerns about the obstacles still facing global recovery.

The peso MXN=MEX01 lost 1.75 percent to 12.9156 per U.S. dollar, its steepest one-day drop since Oct. 1, spurring the central bank to sell $11 million in dollars in an auction to support the currency.

"This is looking bad. A lot of people went long on the peso once it broke 12.80 last week. Now it looks like they are all running for the door," said a trader in Mexico City.

The IPC stock index .MXX closed down 1.17 percent at 31,710.39 amid the global sell off in riskier emerging market assets, stocks and commodities.

Investor confidence in Dubai took a fresh knock on Tuesday as officials dithered over a rescue for debt-laden state conglomerate Dubai World [DBWLD.UL] and ratings agency Moody's downgraded government-related debt.

The Dubai news hit European bank shares while the euro slid after Fitch Ratings downgraded Greece's credit rating, stoking fear about government deficits.

"This is big risk-off day," said Win Thin, an emerging market strategist at Brown Brothers Harriman in New York.

The dollar rose broadly as investors unwound "carry trades" that involved borrowing the U.S. currency at low rates to finance purchases of higher-yielding currencies and assets.

"There was a huge position skew, not just in Mexico, but in all emerging markets, just short dollars. This dollar move stronger could keep going on for a few more days, or weeks. Who knows?" Thin said.

Before Tuesday's losses, the peso had gained around 9 percent since the beginning of October and rallied to a 13-month high last week.

The peso's gains followed a widely priced-in debt downgrade by Fitch Ratings and increasing confidence in the economic recovery in the United States, Mexico's top trading partner.

The peso broke decisively past the 12.80 level last week for the first time since losing around one quarter of its value late last year during the credit crisis.

Traders said a lot of traders had bet on further appreciation of the peso, but more losses in coming days could spur traders to unwind more of those bets, pushing the peso back toward 13.10 per U.S. dollar.

In local stock trading, shares in America Movil (AMXL.MX), Latin America's biggest wireless operator, lost 1.79 percent to 30.15 pesos while miner Grupo Mexico (GMEXICOB.MX) shed 2.44 percent to 29.19 pesos. (Reporting by Michael O'Boyle, Editing by Chizu Nomiyama)