Both teams were locked 1-1 after regulation time after Nigerian striker Kalu Uche (6th minute) opened the scoring for Delhi only for Trinidad and Tobago player Willis Plaza (35th) to equalise.
There were no goals in the second half as the match headed for extra time.
Plaza helped Churchill take the lead for the first time with a crisp strike in the 106th minute to guide the Goa team into the final round where they will take on I-League heavyweights Mohun Bagan on April 1.
The game got off to a flying start as Delhi took the the lead as early as the sixth minute.
Uche made the most of the space afforded to him, unleashing a screamer from the edge of the box with the goalkeeper was caught off the line and past defender Osagie Monday into the net.
Churchill struggled to get any kind of momentum after the early jolt allowing ample time to Delhi midfielders to control play at the centre of the park.
As the game neared the half-hour mark, Churchill began to find momentum and Nicholas Fernandes even found the back of the net after a neat buildup play, only for referee to rule the Goan winger offside.
Churchill though were not denied minutes later when Plaza stabbed home a inch-perfect cross from Fernandes.
After halftime, Delhi got a chance to reclaim their lead when Mirabaje carved open Churchill's defence to find for Seityasen Singh but Monday came to the rescue in time.
Plaza, brilliant on the night, troubled Delhi's defence and came close on a few occasions.
Both teams could not be separated at the end of the full time as well as first half extra time.
Right at the beginning of the second half, a long ball from Meitei was brilliantly brought down by Plaza, who kept his composure to calmly slot it past Xabier.
Delhi threw the kitchen sink at Churchill in the dying minutes of the match but the I-League straggleres held fort and scripted an unlikely victory.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
