Key players Angelo Mathews, Thisara Perera and Lasith Malinga were not selected in Sri Lankan starting 11.
India named its strongest available team, with Sachin Tendulkar opening the innings with Gautam Gambhir.
The 11th edition of the Asia Cup also involves Bangladesh and Pakistan.
On Sunday, Pakistan beat Bangladesh by 21 runs in the opening match.
India has won the competition five times, while Sri Lanka won it four times. Both teams recently featured in the limited-overs tri-series in Australia, where the Sri Lanka lost the finals series 2-1 to Australia.
Lineups:
India: Gautam Gambhir, Sachin Tendulkar, Virat Kohli, Rohit Sharma, Suresh Raina, Mahendra Singh Dhoni (captain), Ravindra Jadeja, Irfan Pathan, Ravichandran Ashwin, Praveen Kumar, Vinay Kumar.
Sri Lanka: Tillakaratne Dilshan, Mahela Jayawardene (captain), Kumar Sangakkara, Dinesh Chandimal, Upul Tharanga, Chamara Kapugedara, Lahiru Thirimanne, Perveez Maharoof, Nuwan Kulasekara, Suresh Lakmal, Seekkuge Prasanna.