Dinesh Karthik top-scored with 66 as India made 268-6 after electing to bat in the day-night final, before the defending champions and hosts were shot out for 187.
India, who last won the region's premier one-day prize during the 1994-95 season, denied Sri Lanka a hat-trick of titles following their victories in 2004 and 2008.
Nehra claimed four wickets, including two in one over, as Sri Lanka were reduced to 51-5 by the 16th over before being bundled out in the 45th over.
India never looked back after hard-hitting opener Tillakaratne Dilshan was dismissed off the fifth delivery, holing out to mid-on off seamer Praveen Kumar.
Kumar, who made use of windy conditions to swing the ball, bowled an unchanged opening spell of nine overs in which he conceded just 29 runs.
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Fellow seamer Zaheer Khan bowled Upul Tharanga, before Nehra wrecked havoc by having Mahela Jayawardene and Angelo Mathews caught behind in the 14th over.
Nehra also removed Sri Lankan captain Kumar San