Young Dempo forward Mandar Rao Desai (44th minute) and captain Sunil Chhetri (81st) scored either side of halftime to ensure India finished their China tour with an all-win record. The visiting side had beaten Jiangsu Sainty in their first match.
India could have scored more had substitute Seminlen Doungel's shot not come off the crosspiece, an AIFF release said.
Shanghai East Asia are currently placed fourth in the Chinese Super League points table with 41 points from 23 outings.
India though were rewarded for their efforts in the dying minutes of the half, when Mandar ghosted behind the opponents' backline to latch on to a neat pass from Chhetri. The Dempo lad then placed his shot perfectly to beat the keeper at his first post.
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India doubled their advantage in the second half, this time Chhetri getting on the end of a wonderful move involving his Bengaluru FC compatriots Siam and Robin. The India and Bengaluru FC captain struck low to the keeper's left after Siam put Robin through with a measured pass which the tall striker laid on for Chhetri.
Striker Bala Devi (6th, 10th and 34th minutes) notched up a hat-trick and midfielder Premi Devi added another as India dominated their opponents from start to finish.