That's a good sign for December's jobs report, which will be released Friday.
The survey covers businesses that employ 90 percent of the workforce, including retail, construction, health care and financial services firms.
Anthony Nieves, chairman of the ISM's services survey, said the declines in orders and business stockpiles likely occurred after "a little bit of excess" had built up in anticipation of the winter holidays. He expects the orders index to recover in the coming months.
The rise in hiring suggests companies are still "confident enough in the pipeline to add jobs," he added.
The drop in new orders would point to slower growth, if it continued, economists said. But most expect the decline will be temporary.
"This will likely prove to be transient, rather than the start of a new trend," said Thomas Feltmate, an economist at TD Bank. "As ... consumer confidence continues to improve, we expect to see an acceleration in consumer spending in 2014, which should prove supportive of future supplier orders."
Other economists noted that severe weather last month could have hampered business for many firms. One company in the arts, entertainment and recreation industry told the ISM that "both customers and employees were unable to reach the workplace" because of bad weather.
Service companies have grown at a modest pace this year. It has averaged 54.7 over the past 12 months.
The survey typically tracks growth in consumer spending, which drives 70 percent of economic growth.
Spending by consumers was restrained for most of last year. But Americans have opened their wallets a bit more in recent months. That could push the index higher in 2014.
Retail sales posted healthy gains in November and December, according to government figures. The biggest increases were at auto dealers, furniture stores, and at electronics and appliance stores. Those outlets have benefited as Americans have purchased more homes and cars. Online shopping has also grown at a strong pace.
However, traditional retailers, such as department stores and clothing stores, haven't benefited as much. Many were disappointed by this season's holiday sales.
The dip in the services index comes after the ISM said Thursday that its manufacturing index remained near a 2 ½-year high in November. Measures of new orders and employment grew at a faster pace, pointing to higher output in the coming months.
The economy expanded at a 4.1 percent annual pace in the July-September quarter, buoyed by a big increase in companies' stockpiles. That was the fastest pace in nearly two years. Growth was likely slower in the October-December quarter because inventory building probably didn't boost growth by as much.