Pablo Counago scored twice (14th and 17th) while Jordi Tarres (57th) and Cheng Siu Wai (80th) struck once each for Kitchee in their penultimate Group E match at Balewadi Sports Complex which is being used by Churchill as their home venue.
After today's defeat, Churchill are now on four points from five matches and they are out of reckoning for a last 16 knockout berth.
Counago opened the scoring for Kitchee with his first goal of the campaign in the 14 minute.
Kitchee came close to a third, two minutes before half-time as Cheung Kin Fung's strike crashed into the crossbar.
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Henri Antchouet finally created a chance of note for Churchill Brothers six minutes into the second half, but the Gabonese striker was denied by Kitchee goalkeeper Wang Zhenpeng.
And six minutes later, Tarres added a third for the visitors as the Spaniard extended his record of scoring in every game during the AFC Cup campaign having scored twice as Kitchee beat Churchill Brothers 3-0 in February.