Edu scored in the 67th minute off a set-piece movement while Chhetri cashed in on a defensive blunder from Mehrajuddin Wadoo in the third minute of stoppage time to get full points for the 'Blues' in what was their first ever appearance in the cash-rich league.
After a barren first-half, it was former Zaragoza B team player Edu, who broke the deadlock. After playing a one-two with Udanta Singh off a corner, he took a left-footer as Mumbai goalkeeper Amrinder Singh was beaten at near post.
Chasing a long ball, Chhetri put pressure on stopper Mehrajuddin, whose miscommunication with a surging Amrinder saw the Indian captain latch onto the free ball before slotting it home with precision.
Chhetri was awarded Man of the match for his brilliant performance as he was a livewire upfront.
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Bengaluru FC coach Alberto Roca deployed the traditional 4-4-2 format with Chhetri and Fedor upfront.
The home team dominated the proceedings by making several attempts at the goal but Amrinder Singh kept the sheet clean during the first 45 minutes.
The cross was intercepted by Marcio Nascimento Rozario much to the relief of Amrinder.
Although BFC played agressively, their centre backs Juanan Gonzalez and John Johnson flanked by side backs Harmanjyot Khabra and Rahul Bheke performed admirably.
In the 23rd minute, Fedor sent a cross from right flank but Chhetri's volley was off the mark.
The shots of Chhetri and Lenny Rodrigues, in 27th and 29th minutes also went haywire.
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