Attacker Riga Mustapha (15th minute) gave Pune FC the lead with a penalty kick conversion before striker Miljan Mrdakovic (38th) pulled the hosts level in the first half.
Second half strikes from medio Closa Gonzalez (61st) and Mrdakovic (69th) handed Tampines Rovers all three points.
With this loss, Pune FC slipped down to fourth place in Group-H behind leaders Kitchee SC (7 pts), Nay Pyi Taw FC (4 pts) and Tampines Rovers (3 pts) midway through the group-stage.
After soaking pressure in the opening exchanges, Pune FC took the lead at the quarter-hour mark.
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As Pavlovic jumped to head a high rising ball inside the box, Tampines goalkeeper Hyrulnizam Juma'at fumbled and continued to head out hoping to control. In doing so, he ended up pulling down Pavlovic and the referee pointed to the spot.
Riga stepped up and coolly converted from the spot sending Hyrulnizam the wrong way while slotting home at the bottom left corner.
Six minutes past the half hour mark, Pune FC once again went close. Winger Gabriel Fernandes did well to slide in a cross from the right, but the delivery fell just short for Pavlovic, one-on-one with the keeper inside the box.
At the other end, Tampines pulled level to restore parity. Keeper Amrinder Singh and skipper Anas Edathodika's mix up resulted in a back pass inside the penalty box and the referee awarded an indirect freekick on the edge of the 6-yard box.
At the other end, Pune FC began to push up and went close through Pavlovic, Riga and Gabriel. However, poor finishing in the final third let the trio down as both sides went into the break tied at 1-1.