Kitchee took the lead after just three minutes when Liang Zicheng found the back of the net, but Jamil Ali hit back for Great Eastern-YEO's S.League champions Tampines midway through the first half when he nodded home from close range.
Liang then put the hosts 2-1 up in the 62nd minute, before Jordi Tarres, who had missed a penalty in the first half, capped off a good night for Kitchee four minutes later.
Tampines coach Steven Tan remained upbeat despite the loss, and is already targeting a win in their next AFC Cup game against Song Lam Nghe An.
"I couldn't ask for a better performance from my team," Tan said, according to the AFC's official website. "But we were punished in the end for a naive defensive mistake.
"It is something that we will have to work on.
"However, Kitchee are a good team and it was very difficult to keep pace with them. Hopefully we can improve and get a win against Song Lam Nghe An in our next game."
Kitchee coach Josep Gombau paid credit to the visitors, whom he felt matched his side for much of the game.
"It was a very good game from both teams and I thought we were quite equal," Gombau said.
"I am happy that my team could play their own style of football, but we have to continue to work hard to ensure that we qualify for the next round."
In Tuesday's other Group F encounter, Malaysia Super League outfit Terengganu recorded a 1-0 win over Vietnam champions Song Lam Nghe An.