The friendly took place in Montego Bay with Shaw and her team-mates looking to return to winning ways after a run of difficult defeats to France, Brazil and Chile.
After almost half an hour, the hosts finally broke the deadlock through Birmingham City’s Siobhan Wilson.
But the match still proved to be a tricky affair despite Jamaica’s one-goal lead. And up stepped Shaw who offered a sign of relief with two goals after the restart.
On 55 minutes the City striker doubled Jamaica’s advantage before a late third on 82 minutes confirmed her nation’s win.
They will take on South Africa again, in another friendly, in Jamaica’s final international fixture of 2024.
The game will commence at 00:30 (UK) on Tuesday 3 December. A round-up of the match plus other international results which include City stars will be available on mancity.com and the Official Man City App.
Elsewhere, Leila Ouahabi played the full 90 minutes of Spain’s 5-0 friendly win over South Korea.
The City defender gave an impressive display and assisted the Spaniards’ fifth and final goal at the Estadio Municipal Cartagonova.
A Clàudia Pina header on four minutes put the hosts ahead as she turned home a Mariona Caldentey cross.
Ouahabi came close on 16 minutes with a shot from the centre of the box that flew wide.
Amaiur Sarriegi doubled Spain’s lead on the half-hour with a right footed shot from Patri Guijarro’s pass.
Aitana Bonmatí all-but sealed victory in first half added time with a smart finish inside the box.
Further goals from Vicky López on the hour and three minutes into added time – the latter from Ouahabi’s corner.
The game was watched by a crowd of 8,672.
Kerstin Casparij and Jill Roord both started on the bench for the Netherlands in their friendly against China at the Sparta-Stadion Het Kasteel in Rotterdam.
Jin Kun gave China a 34th-minute lead – an advantage they took into the break.
Kaptein levelled for the Dutch on 66 and Roord came on three minutes later.
It took the City midfielder just six minutes to find the net with a smart finish into the bottom left-hand corner.
Further goals from Beerensteyn (81) and Brugts (84) completed a 4-1 win for Netherlands.