Dempo's Japanese star Ryuji Sueoka was the star of the show for his side, bagging a brace, while Roberto Mendes 'Beto' da Silva's strike for Churchill ultimately proved to be nothing more than a mere consolation who finished third in India's elite division last season.
Sueoka opened the scoring as early as the second minute, the striker seizing on a Sandip Nandy error to break the deadlock.
Despite their fine start, Dempo then struggled to take a firm grip of the game. Indeed, Churchill dominated for long spells throughout the first half and went close through two Beto headers and a Steven Dias effort, although Anthony Pereira did hit the crossbar for the hosts.
Churchill's resilience was, however, to be rewarded shortly after the break when Tomba Singh's long range shot was only parried into the path of Beto by Dempo goalkeeper Subhashish Roy Chowdhury. The Brazilian tapping home to restore parity.
Churchill duly battled hard to deny Dempo the ball, but the defending champions had the last laugh when Sueoka fended off challenges from Denzil Franco and Dharmaraj Ravanan to apply the finishing touch to a measured Pereira cross.
Meanwhile, Kolkata giants Mohun Bagan suffered a shock 2-0 defeat at the hands of hosts Shillong Lajong.
A crowd of some 14,000 spectators will no doubt have been impressed by the display of Des Bulpin's Shillong, a side who routinely proved more than a match for their illustrious opponents and thoroughly deserved their win.
With DPR Korea defender Min Chol-son starting alongside Wailadmi Passah in defence for Shillong, the home team more than held their own in the first period, although they had to wait until the 63rd minute to take the lead, substitute Boithang Hoakip on hand to score his side's first league goal of the new campaign.
With Bagan's foreign recruits Okolie Odafa and Tolgay Ozbey looking strangely out of sorts, Shillong wrapped up all three points in second half injury time courtesy of Lalramluaha Hmar.
Elsewhere, I-League debutants United Sikkim twice came from a goal down to upset Salgaocar 3-2 in a thrilling match at the Paljor Stadium in Gangtok.
After a dull first 45 minutes, the game came alive in a terrific second half, Angel Guirado heading home to give the Goan club a 50th minute lead.
The Snow Lions responded swiftly and restored parity two minutes later when Salgaocar goalkeeper Karanjit Singh could only parry striker Buddiram Tudu's shot and Nurudeen Salau scored from the rebound.
Bloodied and yet unbowed, Salgaocar, coached by Moroccan Karim Bencherifa, fought back to regain the lead through Milagres Gonsalves on 57 minutes.
The advantage was not to last though as first Lineker Machado drew United Sikkim level, before defender Sandesh Jhingan rose highest to nod home Ashish Chettri's free-kick and seal all three points for his side.
In Saturday's final match, Pailan Arrows edged past Mumbai FC 3-2 to begin their latest I-League venture with a win at Kolkata's Salt Lake Stadium.
Arrows opened the scoring in the 34th minute when Holicharan Narzary made the most of a mistake by Mumbai FC custodian Sanjiban Ghosh.
Undaunted, the visitors hit back in the 39th minute when a clearance from Arrows custodian Ravi Kumar cannoned off Afghanistan forward Haroon Ameri. ND Opara was on hand to mop up the rebound and score.
Mumbai, who finished 11th in the I-League standing last time out, then went ahead shortly before the break thanks to a blistering shot from James Singh.
However, a rejuvenated Arrows turned things around after the break.
The AIFF developmental side went ahead thanks to a Milan Singh penalty in the 53rd minute after defender Justin Stephen had brought down Arrows' Pronoy Halder. A howler from Mumbai keeper Sanjiban Ghosh then allowed Holicharan Narzary to seal the deal for Pailan Arrows 14 minutes from time.