Pelissari's 87th minute strike ensured Marco Materazzi's men's maintain their pole position in the eight-team league table with 22 points from 12 games -- six points clear of second placed Atletico de Kolkata.
Blasters still hold onto their fourth place in the table with 15 points from 12 games.
There weren't too many eye-catching moments but 'Super-Sub' Pelissari's strike just 13 minutes after being introduced into thick of things.
It was corner that Blasters had earned at the other end and one saw Pelissari receive a clearance at the middle third in his own half. It was the start of 50-metre down the middle sprint as rival defenders chased shadows.
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The 61,000 partisan crowd went into pin-drop silence as they simply couldn't believe what hit them.
The Chennaiyin, who are playing without their talismanic Brazilian Elano Blumer showed that they have solid bench strength as they snatched full points in a difiicult away game.
It couldn't have been more delightful for team's co-owner Abhishek Bachchan, who was seen in the VIP box along with his wife Aishwarya Rai Bachchan.
With Chennaiyin's French goalie Gennaro Bracigliano coming out of his charge, Hume's placement in haste was off target.
Blasters also received a setback when their skipper-cum-manager David James pulled a hamstring and was replaced by Nandy as early as 20th minute of the match.