In a match that was seen as a battle between the two Englishmen coaches -- Trevor Morgan (East Bengal) and David Booth -- the home outfit struggled to get the match-winner as the Goans put up a dogged defensive display.
But Chidi struck in the 66th minute with a right-flank attack as his shot took the deflection of opponent Rocus Lamare before finding the back of the net.
Unbeaten from eight matches, East Bengal now have 20 points, while Salgaocar remained at the bottom half with 10.
East Bengal, who struggled to get past the Salgaocar defence, finally got one past the Goans when Chidi's right-footer took a deflection off Lamare's hand before entering the goal.
East Bengal could have easily gone one-up at the break but Orji Penn missed an easy chance in a 32nd minute when the Nigerian squandered a six-yard shot from Manandeep Singh's left-sided cross.
Manandeep, who assisted Chidi in the forward line-up, had a poor day, missing two headers but credit should also be given to the alert Salgaocar defence led by Luciano Sabrosa.
Salgaocar goalkeeper Karanjit Singh also stood tall under the bar thwarting some good moves by East Bengal but the one miss proved costly for the side on a transition phase under new coach Booth who replaced Karim Bencherifa at the helm.
