The left-handed duo put on 181 for the second wicket to lead Sri Lanka to 256 for two in their first innings before heavy rain stopped play 22 overs early at the Galle International Stadium.
Sangakkara made 103, his 22nd Test century and fourth against India, while Paranavitana notched up his maiden ton to remain unbeaten on 110 at the close.
Some 15,000 home fans were on hand to watch the final Test match for world bowling record holder Muttiah Muralitharan, who needs eight more scalps to reach the 800-wicket mark.
Sri Lanka's sports minister Chandrasiri Ratnayake presented Muralitharan with a silver plaque before the start of play, which was delayed by 30 minutes due to a wet outfield caused by heavy overnight rain.
Posters hailing Sri Lanka's favourite cricketing son as the 'greatest bowler ever' were plastered around the ground alongside giant pictures of the off-spinner.
India's depleted bowling attack, missing the injured pace duo of Zaheer Khan and Shanthakumaran Sreesanth