* Banco de Mexico cuts benchmark credit costs to 3.75 pct * Move defied analysts' expectations for unchanged rates * Policymakers set weak growth against inflation, peso By Michael O'Boyle and Alexandra Alper MEXICO CITY, Sept 6 (Reuters) - Mexico's central bank unexpectedly lowered borrowing costs on Friday to counter a slump in growth, keeping the door open to a further cut and leaving the weak peso vulnerable if the United States starts to unwind stimulus. The Banco de Mexico cut its benchmark rate by 25 basis points to 3.75 percent, the lowest level since the key rate was introduced in early 2008, in a move that was predicted by few economists. But investors welcomed the move to shore up Latin America's No. 2 economy. While the peso at first wilted on the cut, it bounced back higher while bonds and stocks rallied. Economists had doubted Mexico would move ahead of the U.S. Federal Reserve, which could begin winding down its $85 billion-a-month bond buying program as early as this month. Such a move could spark volatility in global financial markets. But policymakers said inflation would keep cooling in the coming months while risks to growth had deepened significantly compared to the central bank's previous forecasts. Mexico's economy contracted for the first time in four years in the second quarter and policymakers said growth next year would also likely be weaker than policymakers had expected. "Hence, a wide degree of slack in the economy is expected for a prolonged period. This points to a path for inflation in the coming months below the one previously predicted," the central bank said in a statement accompanying the decision. The surprise cut comes just before the government is set to unveil a proposed tax overhaul that is a key component of a wider economic reform package. However, higher taxes could dampen growth and fuel inflation in the short term. The central bank said any impact from the tax reform would be transitory and was unlikely to spur knock-on effects on prices. Bond prices surged after the move, driving down yields sharply while stocks pared early losses to rise around 1 percent on expectations that lower borrowing costs would help companies better weather the current soft patch in the economy. The central bank gave few hints on whether it was planning to keep cutting interest rates but analysts said they had left the door open to another cut if growth continues to falter. "Mexican data is going to keep being bad, so you cannot rule out another cut," said Salvador Orozco, a strategist at Santander in Mexico City. Barclays called for another 25 basis point cut in October and Citigroup-unit Banamex also said there could be another move lower if proposed tax hikes are modest. Still, other analysts said stronger growth in the United States, Mexico's top trading partner, could help Mexico's economy and make another cut unlikely. The finance ministry has said it is expecting a pickup in the second half of the year. "ROLLING THE DICE" Cheap dollars spurred a tide of investment into emerging markets in recent years, but those same markets have been punished since May on concerns that U.S. stimulus could be reduced. Mexico's peso has lost about 9 percent since then. A slowing in bond purchases by the Fed could push up returns on U.S. assets, draw investment back to the United States and hurt the depreciating peso even more. That could risk higher inflation if import prices rise. Lower benchmark interest rates in Mexico reduce the appeal of local assets to yield-hungry investors, and the central bank's cut could make the peso more vulnerable to a Fed move. "They are rolling the dice in this sense," said Enrique Alvarez, an analyst at IDEAglobal in New York, who said policymakers are betting they can navigate a wind-down by the Fed and come out with stronger growth in the end. "So I think it is a good risk to run. It is a calculated risk." The peso's recovery on Friday signaled many investors were comfortable with the risk the bank was taking. After growth contracted in the second quarter, the government slashed its growth outlook to 1.8 percent this year from a previous 3.1 percent estimate. Meanwhile, inflation has fallen back below the central bank's ceiling of 4 percent and policymakers said weak growth would help further cool price pressures. Mexico's central bank cut its benchmark rate for the first time in nearly four years in March in what was seen as a bid to curb massive foreign investment flows. But policymakers then held rates steady after a surge in some fresh food prices drove inflation above 4 percent.