The hosts were brushed aside by the S.League champions, who recovered from going behind to keep their bid to qualify for the next round of the AFC Cup on track
The S.League champions moved to second with the triumph and are now four points behind Hong Kong's Kitchee SC, while Pune remain bottom with two points from four matches.
Salim Moin made three changes to his side with Luis Closa, Anaz Hadee and Shariff Samat all being drafted into the starting 11, while Pune restored first choice custodian Amrinder Singh, central defender Anas Edathodika and midfielder Anthony D'Souza to theirs.
It was the visitors who took an early lead through Miljan Mrdakovic's third goal in two games in the competition, the Serbian striker heading in Jamil Ali's superb cross after only five minutes for his 10th goal of the season.
However, having beaten the Red Lizards 3-1 back in Singapore two weeks ago, the Stags had to repeat the trick the hard way here as the hosts battled back.
Mustapha Riga rounded goalkeeper Hyrulnizam Juma'at after latching on to Douhou Pierre’s inch-perfect through ball to level the scores seven minutes later, before setting up Anthony D’Souza for a double whammy 120 seconds later.
The midfielder combined well with Riga on the left before going past three Tampines defenders and smashing a powerful right-footed effort into the roof of the net, sending the home fans wild.
Hyrulnizam had to deny the same player just past the half hour, before doing well to save from Mirjan Pavlovic seven minutes later.
Those saves proved crucial, as Tampines got themselves back on equal terms two minutes before half time.
Mustafic Fahrudin's free-kick from deep found Jamil in the box on the right and the winger took a touch before placing the ball past Amrinder and into the bottom corner.The Stags went from strength to strength and veteran forward Aleksandar Duric put them ahead for the second time in the game on 57 minutes, tapping home from close range after Closa got to the byline and pulled the ball back.
Things got worse for Pune as when Zohmingliana Ralte was deemed to have handled Duric's cross three minutes later. The referee pointed to the spot and skipper Mustafic made no mistake, sending his spot-kick into the bottom left corner to make it 4-2.
Mike Snoei made two substitutions in the 63rd minute as he replaced Douhou and Mumtaz with Thongkhosiem Haokip and Gurjunder Kumar respectively, but it was Tampines who scored again to kill off any hopes of a comeback.
Jamil stormed right at the heart of the opposing defence before threading Duric through and the 43-year-old made no mistake with a composed finish to put the gloss on the scoreline, as Tampines went away with a crucial victory.