Clayvin Zuniga's 16th-minute strike was enough to give Fernando Varela's side all three points in a game full of chances.
Fernando Varela's side have had some time to rest, and with top scorer Clayvin Zuniga back, they will be looking forward to getting back to winning ways.
A win on Thursday will extend Punjab's lead to four points over Real Kashmir, who still have a game in hand.
With the result, the Punjab side have now displaced Churchill Brothers on the summit of I-League points table with 14 points from eight outings — one point ahead of the Red Machines, who have played one game less.
I-League 2021: Churchill Brothers' top-of-the-table clash with Real Kashmir ends in stalemate; Mohammedan SC win
The top of the table clash between Churchill and Real Kashmir was certainly embedded with fireworks right from kick-off as neither team held back in the opening minutes of the match.
Both the teams create scoring chances but the match ended in a stalemate as neither side was able to convert inside the box.
Despite the draw, Churchill managed to maintain their position at the top of the I-League standings with 11 points from five matches. TRAU are second in the standings with seven points from five games.
In a match largely dominated by Fernando Varela's men, first-half strikes by Luka Majcen (19th minute) and Bryce Miranda (36th) proved enough as Churchill grabbed their third win of the season.
If the results go Churchill Brothers' way on Monday, the Goan club could go five points clear of the second-placed team.
I-League 2021: Real Kashmir held to draw by Sudeva Delhi; Clayvin Zuniga powers Churchill Brothers to win
Goals by Komron Tursunov in the second minute and Helder Lobato in first-half stoppage time were cancelled out by headers from Nikhil Kadam and Hira Mondal in the 58th and 68th minutes respectively, as both the teams shared points at the end of the 90 minutes.
I-League 2021: Gokulam Kerala fight back to beat Punjab FC in seven-goal thriller; Churchill Brothers hold Mohammedan
In a tactical match where chances were few and far between, both teams cancelled each other out in the middle of the park, sharing the spoils of the match.
I-League 2021: Hat-trick hero Clayvin Bernardez powers Churchill Brothers to win; Real Kashmir, TRAU play out draw
Bernardez struck in the 35th, 58th and 69th minutes while Majcen was on target in the second and 75th minute.
I-League 2021: Churchill Brothers face tricky opponents Indian Arrows as Goa-based outfit seek winning start
Churchill Brothers are eyeing their third trophy in the coming season and head coach Fernando Varela, who was in the Gokulam Kerala FC dugout last season, stressed on the importance of making a winning start.
AIFF conducts online seminars on coaching methodologies, chalks out plans for coach's education in India
The online seminars conducted by AIFF head of Coach Education, Savio Madeira on 1, 3 and 8 April were attended by 14 instructors from all over the country.
The Snow Leopards are fourth in the league with 22 points from 15 games while TRAU are fifth with the same number of points, but having played two games more
I-League 2019-20: Henry Kisekka last-minute goal for Gokulam Kerala dents Churchill Brothers' hopes of second place finish
Henry Kisekka scored in the last minute as Gokulam Kerala FC beat Churchill Brothers 2-1 in a thrilling match of the I-League on Sunday.
I-League 2019-20: With draw against Chennai City FC, Mohun Bagan better own record of longest unbeaten streak in a season
Mohun Bagan have gone on a 13-match unbeaten run in the ongoing I-League season
I-League 2019-20: Jaime Colado's 95th-minute spotkick sees East Bengal rescue point against Churchill Brothers
East Bengal failed to make use of their opportunities till late in the match before Colado struck off a rebound after his penalty was thwarted by James Khitan in 95th minute
I-League 2019-20: Favourites Mohun Bagan look to build on six-match winning streak in away clash at TRAU FC
TRAU FC forged a seven-game unbeaten run and rose to third on the points table but are now winless in five games
Churchill Brothers notched up a 2-1 victory over Real Kashmir FC and rose to the third spot in the I-League table in Margao on Wednesday.