The HSBC Services Purchasing Managers' Index (PMI), compiled by Markit, rose to 51.6 in September from 50.6 in August, reversing a slowdown seen in the previous two months.
A reading above 50 signifies growth while anything below denotes contraction. The new business sub-index climbed to 52.4 from 51.9, signalling robust demand.
"Service sector activity bottomed out in September thanks to stronger new business flows," said Frederic Neumann, co-head of Asian economic research at survey sponsor HSBC.
In what might also give some respite to an economy that has long struggled with high inflation, the sub-index measuring output price growth fell to a near four-year low.
India's annual consumer price inflation eased in August to 7.80 percent from 7.96 percent in July.
Wholesale prices also rose at a slower clip during that month.
But the Reserve Bank of India doesn't appear to be in a hurry to ease monetary policy and hinted last week that it won't do so until it is confident that consumer inflation can be reduced to a target of 6 percent by January 2016.
Activity in the private sector has expanded steadily since May, when Prime Minister Narendra Modi won a landslide mandate that created a wave of optimism over India's economic prospects.
But the lack of sweeping reforms by Modi's government so far has taken the sheen off those hopes.
The survey showed firms' confidence regarding future business grew at the slowest pace in a year last month.
"A pick up in reform effort is sorely needed to put growth on a firmer footing and address supply side risks to inflation," Neumann said.
(Reporting by Deepti Govind)
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