Chhetri, who once again combined very well with Haitian Sony Norde and compatriot Subash Singh, scored from the penalty-spot in the 25th and 48th minutes, while volleying home from close range in-between in the 40th minute, to complete the second hat-trick of the season. Chennayin FC's Steiven Mendoza had scored the first against FC Goa.
The triple strike took the diminutive Indian striker's tally of goals to six - the highest so far in the league this season - and included his double strike against Delhi Dynamos and a lone goal against FC Goa, both won 2-0 by Mumbai.
NEU got their only goal of the game, which neutralised Chhetri's opening goal, through Boithang Haokip in the 29th minute, before playing second fiddle right till the end to the home team.
The third successive victory, all at home, propelled Mumbai to the second spot on the table. They have ten points now, two points behind leaders FC Pune City and level with FC Goa who have an inferior goal difference.
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Both teams missed a few half-chances to score before Mumbai shot into the lead in the 25th minute through a penalty award.
It came off a counter attack when a surprisingly unmarked Chhetri collected the ball on the right side of the field, darted into the penalty area and laid a measured pass to Subhash Singh on his right.
Subhash, without wasting time, crossed to the left. The ball struck the hand of a leaping defender Carlos Lopez leading to a penalty award which was coolly slotted home into the left corner of the goal by Chhetri, the India captain's fourth strike in the last three games.
The ball swerved towards the goal, beating a couple of defenders forming the wall and India custodian Subrata Paul, who was rooted to his spot, on its way in.