By Gabriel Tan at the Clementi Stadium
French forward Julien Durand had given the Bulls a 10th-minute lead before Jung Hee-bong put them in the driving seat when he grabbed a second from the spot two minutes after the break.
However, Rovers refused to give up and pulled one back through captain Aleksandar Duric in the 65th minute, before Mustafic Fahrudin equalised from a penalty of their own five minutes before the end.
And while the hosts would have been forgiven for settling for a point, Jamil, who had came on in the 76th minute, had other ideas and scored a wonder goal three minutes into stoppage time to hand the Stags all three points.
Defending Great Eastern-YEO's S.League champions Tampines came into the game high on confidence after recording consecutive wins over Geylang United in the league and Terengganu in the AFC Cup, with Duric scoring five goals in those two matches.
Nonetheless, the Stags were given a rude shock just ten minutes in when Gombak took the lead through Durand. Hafiz Rahim latched onto a throw-in by Ismail Yunos just inside the Tampines half and played a delightful ball with the outside of his foot into the path of the Frenchman, who held off the challenge of Anaz Hadee before firing past Sasa Dreven.
With Singapore coach Radojko Avramovic watching in the stands, the game provided the opportunity for several players to stake their claim for an international call-up, including teenage Gombak duo Nurullah Hussein and Muhd Nur Na'iim.
Nurullah in particular did his chances no harm, looking extremely steady at left-back early on despite coming up against the tricky Imran Sahib, while also providing plenty of drive when going forward.
With Mustafic and Gligor Gligorov bossing the midfield, Tampines eventually started to dominate proceedings and were getting plenty of joy down the flanks. However, each time they swung in a dangerous ball, it was firmly dealt with by Bulls captain Obadin Aikhena, who was absolutely dominant in the air.
Duric was starting to cut a frustrated figure up front due to the lack of service but he did come close in the 22nd minute when he met a corner from Gligorov and flicked his header towards the far post, only to see Aikhena clear off the line.
But despite Tampines enjoying the lion's share of possession, the Bulls were looking extremely dangerous on the counter and twice came close to doubling their advantage before the break.
First, Ismail somehow managed to scuff his shot wide from four yards out after a good cross from Jung, before Hafiz picked up a loose ball in the box and fired one goalwards, only to see it blocked by some desperate defending.
Nonetheless, it took Gombak just two minutes after the break to go two up, although it came under slightly controversial circumstances.
Following a lapse in concentration by the Tampines backline, Jung picked up the ball inside the area and went down under an innocuous challenge from Jufri Taha. Referee Mohd Yazeen immediately pointed to the spot, much to the dismay of the home fans, and the South Korean picked himself up and confidently dispatched his spot-kick into the back of the net.
Needing a quick response if they were to get anything out of the game, the Stags started to pile on the pressure and were unlucky not to pull one back just six minutes later, when Ahmed Fahmie sent a volley crashing off the crossbar after a nice cross by Sazali Salleh.
Five minutes later, the woodwork came to Gombak's rescue again; this time keeping out a sublime freekick from Mustafic which had Zaiful Nizam well beaten in the Bulls goal.
However, with Tampines pushing more men forward, Gombak were always going to pose a threat on the counter and they nearly added a third on the hour mark; Jung forcing Dreven into a smart save after he raced onto a long ball by Aikhena.
Then in the 65th minute, the Stags finally pulled one back when substitute Davor Piskor found Fahmie inside the box with a clever ball. The 24-year-old forced Zaiful into an excellent stop with a snapshot, but Duric was on hand to stab home and reduce the arrears.
And the 41-year-old nearly grabbed another five minutes later when he turned his opponent smartly on the lefthand side of the area, only to fire his shot against the outside of the post.
The Gombak defence was now under severe pressure, with Aikhena having to be alert to get a toe on the ball after Fahmie found himself one-on-one with Zaiful four yards out.
It was thus unfortunate that the Gombak captain, who had had an exceptional game up to that point, turned from hero to villain in the 85th minute, after he was adjudged to have tugged Duric back in the box. Again, Yazeen pointed to the spot without any hesitation, and up stepped Mustafic who confidently sent his penalty straight down the middle to level the scores.
But just when a draw looked like an acceptable result for Tampines, Jamil picked up the ball on the left deep in injury time and headed straight for goal at full speed, dancing past three challenges before slotting past Zaiful to cap off a remarkable comeback for the defending champions.
Tampines Rovers: Sasa Dreven, Anaz Hadee, Benoit Croissant, Jufri Taha (Ali Hudzaifi 53'), Imran Sahib (Jamil Ali 76'), Mustafic Fahrudin, Sazali Salleh (Davor Piskor 59'), Gligor Gligorov, Ismadi Mukhtar, Ahmed Fahmie, Aleksandar Duric.
Gombak United: Zaiful Nizam, Ismail Yunos (Fairoz Hasan 83'), Walid Lounis, Obadin Aikhena, Nurullah Hussein, K. Vikraman (Samuel Benjamin 73'), Christopher Anderson, Muhd Nur Na'iim (Adrian Dhanaraj 53'), Julien Durand, Hafiz Rahim, Jung Hee-bong.