The hosts were all fired-up after they held Dempo FC 2-2 last week and played aggressively, but were unlucky not to take home full points.
Captain Eugeneson Lyngdoh shot a dead right footer into the left flank, netting the first and only goal for the home side in the 25th minute.
Barely two minutes later, Churchill's Balwant Singh netted in a high ball missed by Rangdajied's goalkeeper to equalise.
A 7000-strong crowd cheered their team as Rangdajied created many opportunities and dominated the proceedings in the first half.
Changing tactics after the lemon break, Churchill's attempts were foiled several times as both teams continued chasing points.
Hugo Alves' free kick just outside the box hit the crossbar in the 55th minute and Rangdajied's keeper Surjay Kumar unleashed a header from Balwant in the 66th minute.