The U.S. in January saw its first dip in overall consumer prices in more than five years. But the economy is far from the precipice of debilitating Japanese-style deflation.

Driven by a tumble in oil prices since mid-2014, the consumer-price index fell 0.1% in January from a year earlier, the Labor Department said Thursday. It was the first year-over-year decrease since October 2009. Prices fell 0.7% from December.

While...