The tourists were comfortably placed after a 51-run stand for the opening wicket between Gautam Gambhir and Virender Sehwag before slipping to 104-3 in their first innings at lunch on the opening day.
Left-handed Gambhir was unbeaten on 57 at the break for his third successive half-century and Sourav Ganguly was not out on two.
Prasad removed in-form opener Sehwag in the opening spell for his first Test victim before trapping former captains Rahul Dravid (10) and Sachin Tendulkar (six) leg-before in the second spell.
He struck in his fourth over when he had Sehwag caught behind after the batsman had contributed a run-a-ball 21 with four boundaries.
Sehwag, who smashed an unbeaten 201 and 50 in the previous Test, looked in punishing mood as he executed some handsome shots against new-ball bowlers Chaminda Vaas and Prasad.
He was dropped on 14 by Malinda Warnapura at short square-leg off Vaas, but failed to capitalise on the chance.
He added only seven more runs before edgin