The better data represents a turnaround after the government said last week that the economy barely expanded in the first three months of the year.
A measure of sales and production surged 7.5 points to 60.9 and a gauge of new orders jumped 4.8 points to 58.2. Both are the highest since August.
The survey covers businesses that employ 90 percent of the workforce, including retail, construction, health care and financial services firms.
A gauge of employment declined, though remained above 50. That indicates that services firms are adding jobs, but more slowly.
Anthony Nieves, chairman of the ISM's services survey committee, said the healthier picture mostly reflects solid increases in consumer demand. But the better spring weather also helped. One survey respondent in the hotel and restaurant industry said that business picked up because of a "break in the weather."
The report is "more evidence of growth reaccelerating after exaggerated weakness a couple of months ago," said Jim O'Sullivan, chief U.S. economist at High Frequency Economics.
Solid job creation has made Americans a bit more confident and more willing to spend. Consumer spending jumped in March by the most in 4 ½ years, as Americans bought more cars, clothes and furniture.
A separate report by the ISM last week showed that manufacturing also grew at a faster pace in April. A measure of hiring jumped to its highest level since December.