The win moves moves Usuthu up to the third in the Betway Premiership standings, four points behind league leaders Orlando Pirates, who have two games in hand.
Arrows, meanwhile, remain tenth on the table - three points behind eighth-placed Durban City.
It was Abafana Bes'thende that applied pressure and they were awarded a penalty in the first-half stoppage-time when Siyanda Ndlovu was fouled in the box.
Junior Dion stepped up for the spot-kick but his effort hit the crossbar as the teams went into the halftime break with the game goalless.
Amazulu then took the ascendancy early after the interval and, in the 56th minute, took the lead when Hanamub received the ball on the left, cut in and unleashed a stunning shot that left goalkeeper Xolani Ngcobo with no chance.
Arrows coach Manqoba Mngqithi looked to his bench to turn things around and introduced Brandon Theron with 20 minutes remaining.
The move almost paid off but Usuthu shot-stopper Olwethu Mzimela produced a brilliant double save deny Theron and then Angelo Van Rooi.
Amazulu then held out in the closing stages to make sure they ended their fixtures for the calendar year on a high note.
Mamelodi Sundowns coach Miguel Cardoso has renewed his criticism of the Premier Soccer League, questioning the timing of their upcoming Betway Premiership match against Orbit College.
Durban City secured their place in the semi-finals of the Nedbank Cup with a 5-4 penalty shootout win over Golden Arrows on Sunday.
Casric Stars' remarkable Nedbank Cup dream continued after the Motsepe Foundation Championship (MFC) side knocked out AmaZulu with a dramatic 2-1 extra-time victory in their quarter-final clash at the Moses Mabhida Stadium on Saturday.
Kaizer Chiefs sporting director Kaizer Motaung Jr. has acknowledged the frustration among supporters as pressure grows on the club's interim coaching duo following a worrying run of results.
