The India football captain was fed decisively on both occasions by Haitian Sony Norde, who had an outstanding game, to score once in each half - in the 13th and 74th minutes - by showing good anticipation and opportunism at the D Y Patil Stadium.
He and his Haitian teammate showed delightful understanding up front and Norde, with his superb ball skills and speed, simply tore apart the rival defense repeatedly to steal the show without scoring goals.
Mumbai, winless in three previous games, drastically revamped its starting eleven by making five changes.
The midfield was re-jigged by bringing in Spanish duo Christian Bustos and Juan Aguilera along with Gabriel Fernandes, and the defense shored up by including Ireland's Darren O'Dea. Subash Singh was the fifth change made by the hosts.
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These alterations looked to have galvanized the home team as the frontline duo of Norde and Chhetri were fed repeatedly from the midfield and kept the rival defense busy through repeated forays.
Mumbai, who had scored their only goal so far during their 1-3 loss to FC Pune City on October 5 and then failed to score in their next two games, found the mark in the 13th minute after a delightful 1-2 between Norde and Chhetri.
Chhetri, who was later booked by the referee, applied the finishing touch with a deft low shot into the left corner of the net, after his strike partner had hoodwinked three defenders to lay the pass to him, much to the delight of the small crowd of spectators.