Electing to bat first, the Indians piled up 277 for five in their allotted 50 overs with openers Goswami and Tanmay denying the Sri Lankans any success in the early overs.
In reply, the hosts were bundled out for 118 in 38 overs with Ravi Jadeja (three for 23) and Iqbal Abdullah (three for 14) emerging the most successful bowlers for India.
Goswami's 77 came from 108 balls with the help of seven fours while Tanmay was more sedate in compiling 66 from 98 deliveries with three hits to the fence.
Delhi lad Virat Kohli and Saurabh Tiwari contributed useful 38 and 32 not out. Tiwary played a cameo with his 32 coming from only 19 balls while dispatching the red cherry over the fence twice. Pradeep Sangwan remained unbeaten on 14.
For Sri Lanka, S Pathirana returned figures of three for 49 from 10 overs.
India U-19 next play Bangladesh on July 22.
India U-19 277 for 5 in 50 overs (S Goswami 77, Tanmay Srivastava 66, Virat Kohli 38, Saurabh Tiwari 32 n o; Pathirana 3 for 49) beat Sri Lanka A 118 all out in 38 overs (Ravi Jadeja 3 for 23, Iqbal Abdullah 3 for 14) by 159 runs.