The left-handed duo, who made hundreds in their victorious first Test in Galle, put on 174 for the second wicket to help the hosts pile up 312-2 by stumps at the Sinhalese Sports Club.
Paranavitana, a 28-year-old playing his 12th Test, revelled in the familiar environs of his home club to follow his maiden century at Galle with a fluent 100.
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Skipper Sangakkara returned unbeaten on 130, his 23rd Test hundred, after he won the toss and elected to take first strike in typically good batting conditions at the SSC.
Both players reached their centuries in the same over, the 71st of the innings, as Paranavitana took three runs off a Pragyan Ojha misfield and Sangakkara lofted Virender Sehwag for a boundary.
Paranavitana was dimissed in the next over, bowled by seamer Ishant Sharma off the inside edge, but former captain Mahela Jayawardene kept Sangakkara company at stumps on 13.
The easy-paced wicket left India's bowlers facing an uphill struggle in hot and humid weather after captain M