JOIN USChurchill, who led 1-0 at half time, scored through Ogba Kalu Nnanna (5th) and Odafe Okolie (65th).
They now have 16 points from eight matches, one point ahead of Dempo Sports Club and Chirag, who have 15 points each, from as many ties.
The hosts took an early lead but lost their way as the visitors started dictating terms in the midfield.
Chirag had a couple of clear chances to equalise in the first half but their forwards lacked direction and sharpness in the absence of key player Emilson Marques.
Nnanna put Churchill ahead in the 5th minute when he headed home a cross from Khan Thang Paite from the left. But the visitors slowly took control of the proceedings and made a couple of moves. S Malsawmtluanga came close to find the equaliser but the goalkeeper thwarted his move.
Chirag kept on pressing for parity and had the best chance in the dying minutes of the first half when a cross from the left by Dhanarajan R into the box was headed out by substitute P C Lalawmpuia. Okolie also had a few chances to score but missed.
Defender Robert Lalthlamuana gave a diagonal pass to Okolie, who dodged past rival defenders Arnab Mondal and Edwardo Chacon and scored the goal, to put Churchill on top of the table.
Meanwhile, Chidi Edeh scored a hat-trick as Mohun Bagan registered a 3-1 away win over Pune FC.
Edek slotted home in the 38th, 65th and 79th minutes before Djidjia Douhou Sey Pierre restored a semblance of pride for Pune in the third minute of injury time.