Despite dominating for the most part, the Protectors found themselves trailing at the break after Gombak winger Mustaqim Manzur scored with a stunning effort from the edge of the area.
Home then spent most of the second half laying siege to the Bulls' goal but were regularly denied by an inspired Zaiful Nizam, before Anzite stole a point eight minutes from time with a well-taken strike.
The match got off to a scrappy start, with the only notable incident in the opening ten minutes being an extended break in play when one of the floodlights at the Bishan Stadium went out.
However, the game eventually restarted and in the 19th minute, Home recorded the first real effort on goal, when Shotaro Ihata met a corner with a powerful header that was kept out by a flying save from Zaiful.
The Protectors continued to dominate proceedings, with midfield trio Shi Jiayi, John Wilkinson and Rhysh Roshan Rai controlling the game, but from nowhere, Gombak took the lead in the 25th minute when Christopher Anderson picked out Mustaqim on the left flank with a neat crossfield pass. The veteran midfielder took one touch to control the ball, sold a dummy to Masrezwan Masturi twice, before hitting a 25-yard effort that sailed over the head of Lionel Lewis and into the back of the net.
Lewis would probably feel he should have done better with that shot as he was caught way off his line, but four minutes later, his team-mates almost made amends for his error when Wilkinson swung in a dangerous freekick, which Mendy turned goalwards with a powerful header. Once again, Zaiful came to the Bulls' rescue with an excellent stop.
Wilkinson then had two half chances to mark his debut with a goal when he was twice presented with a shooting opportunity on the edge of the area, although he fired wide on both occasions.
Two minutes before the break, Gombak had an excellent chance to double their advantage when Mustaqim found space in behind the Home backline after a good run, but his low cross was well smothered by Lewis.
Straight up the other end, Mendy came excruciatingly close to equalising for the Protectors when he was played through by Ihata and fired in a low drive, only to see his effort come back off the post.
Home coach Lee Lim-saeng was clearly not pleased with what he saw in the opening period, and brought on Singapore international Qiu Li right after halftime in a bid to inject some pace and skill down the left.
And seven minutes into the second period, Home must have thought they had equalised when Wilkinson's deep corner found Mendy unmarked two yards out at the far post, only for Zaiful to keep out the Frenchman's effort with a desperate save.
Four minutes later, Gombak captain Obadin Aikhena, who was unbeatable at the back all night long, put in a brilliant sliding challenge to deny Qiu from point-blank range, before Home winger Firdaus Idros twice failed to capitalise after Zaiful spilled routine catches, the only blemishes on an otherwise outstanding display from the Bulls custodian.
Ten minutes from time, Mendy finally beat Zaiful in an aerial challenge but just as the ball looked destined to bounce over the line, Walid Lounis succeeded in a last-ditch attempt to divert the ball to safety.
But just when all seemed lost for Home, Anzite finally found the back of the net two minutes later, when he skillfully trapped a long, searching ball from midfield, before dancing past the challenge of Ismail Yunos, and finishing into the bottom corner, sending the majority of the 1,304 crowd into raptures and salvaging a point for the hosts.
In Thursday's other game, substitute Ruhaizad Ismail struck five minutes from time to help Balestier Khalsa record a shock 1-0 win over defending champions Tampines Rovers at the Jalan Besar Stadium.
Lineups (Home United vs Gombak United)
Home United: Lionel Lewis, Masrezwan Masturi (Hafiz Nor 81'), Franklin Anzite, Kenji Arai, Jeremy Chiang, Firdaus Idros, Rhysh Roshan Rai (Qiu Li 46'), John Wilkinson, Shi Jiayi, Frederic Mendy, Shotaro Ihata.
Gombak United: Zaiful Nizam, Ismail Yunos, Obadin Aikhena, Walid Lounis, Nurullah Hussein, Samuel Benjamin (Amin Rosaddy 71'), Christopher Anderson, Muhd Nur Na'iim (Fairoz Hasan 60'), K. Vikraman (Fareez Farhan 90'), Mustaqim Manzur, Jung Hee-bong.