By Paul Kiernan and Eric Morath

WASHINGTON—U.S. consumer prices rose for a third straight month in June, eating away at sluggish wage growth and sending inflation to its highest rate in more than six years.

The consumer-price index, which gauges what Americans pay for everything from veterinarian services to baby clothes, rose a seasonally adjusted 0.1% in June from the prior month, the Labor Department said Thursday. Excluding volatile food and energy components, prices increased 0.2%. Economists surveyed by The Wall Street Journal had expected a 0.2% uptick from May for both the overall index and so-called core inflation.

Last month’s price increases brought the CPI’s cumulative growth in June from a year earlier to 2.9%, the highest level since February 2012. Core inflation ticked up to 2.3% in June from a year earlier, the highest rate since January 2017.

For the second month in a row, annual inflation fully offset workers’ average hourly wage growth in June, leaving real hourly earnings flat from a year earlier despite falling unemployment and a generally strong economy.

The year-over-year rise in prices was led by energy commodities, following a sharp rise in oil prices earlier this spring. The CPI report showed gasoline prices rising a seasonally adjusted 0.5% in June from May and 24% from a year earlier. Separate data from the U.S. Energy Information Administration showed a gallon of regular gasoline rose in price this spring to reach $2.89 in June, the highest price from the month since 2014.

But prices for other goods and services rose briskly as well.