A reading above 50 signals expansion in services activity over the previous month.
New orders in the Indian services sector expanded for the fifth straight month, and at a faster rate than in August, a sign that demand is picking up amid a revival in business and consumer sentiment as the Modi government launches its reform agenda.
Meanwhile, a combined gauge measuring services and manufacturing in India expanded for the fifth month running, up to 51.8 in September from 51.6 in the previous month.
Cost inflation in the Indian private sector fell to the weakest level since April 2009 in September 2014, adding to the relief of the country's central bank.
"Services sector activity bottomed out in September thanks to stronger new business flows. However, business sentiment continues to deteriorate after a strong post-election uptick", HSBC said.