Fernando made 96 and put on big partnerships, including an 89-run opening stand with Pathum Nissanka, who hit 45, to lay the foundations for Sri Lanka in Colombo.
India's bowlers were led by debutant Riyan Parag, a batsman who bowls off-spin, with three wickets. Parag took the key wicket of Fernando before the Sri Lankan middle-order faltered.
Number three Kusal stood firm from one end and boosted the total with his 59 before he departed in the 49th over off Kuldeep Yadav.
The hosts lead the three-match series 1-0 after they won the second match following a tie in the opener. A win or another tie will give them their first ODI series against India since 1997.
Skipper Charith Asalanka won the toss for the third time and elected to bat.
Axar Patel broke through with his left-arm spin to send Nissanka back but Fernando put together another big stand with Kusal.
Parag, who returned figures of 3-54, also captured Asalanka's wicket for 10 as Sri Lanka slumped from 171-1 to 199-6.
Kusal and Kamindu Mendis, who made an unbeaten 23, put together 36 runs for the seventh wicket and Sri Lanka got 31 runs from the last three overs.
India, led by Rohit Sharma, need 249 to save the series after suffering batting collapses in the first two matches.
