The loss represents a significant blow to Arrows' top-eight chances and they have now collected just a single point from their last five league encounters.
Polokwane City began the brighter of the two sides and were rewarded for their dominance in the 13th minute. Arrows gave possession away sloppily while trying to play out from the back with Mohamed Anas picking up the loose ball and unleashing an unstoppable drive from just outside the box into the bottom right-hand corner.
Soon after, Danny Venter almost equalised for Abafana Bes'thende but his curling free-kick was well saved by Polokwane City goalkeeper George Chigova.
Despite this momentary scare, Rise and Shine were controlling the match as well as looking the more solid of the two sides at the back.
In the 38th minute, midfielder Jabulani Maluleke's free-kick rebounded back to him off the wall and his follow up effort went narrowly wide of Gumede's right-hand post.
Arrows looked like they had been given a stern half-time team talk from coach Steve Komphela as they began the second half in the ascendancy and with renewed vigour.
Lerato Lamola then had a gilt-edged opportunity to equalise in the 60th minute when through on goal but the Abafana Bes'thende forward dallied on the ball too long with the Rise and Shine defence getting back to thwart him just in time.
Arrows almost shot themselves in the foot when Nkosinathi Sibisi was put under pressure by Bongile Booi and facing his own goal sliced his clearance towards goal but was spared the embarrassment by his goalkeeper Gumede, who got back just in time to tip the ball over the bar.
Polokwane City doubled their lead when Bongile Booi rose highest to flick on Maluleke's corner for Charlton Mashumba to prod home into the top corner in the 76th minute.
Soon after, Arrows were caught napping in defence once again allowing Mashumba to sneak in behind but he skewed his volley just inches wide.
Mashumba wasted another opportunity to make the scoreline more flattering but his missed opportunity mattered little as Jozef Vukusic's side emerged with the three points.
Polokwane: 1 Chigova, 22 Mbonani, 20 Phiri, 24 Hlongwane, 27 Motloung, 8 Maluleke, 33 Mvelase, 14 Manaka, 10 Tlolane (Mushumba 75'), 3 Anas (Seabi 63'), 7 Booi (Maluleke 83').
Subs: 9 Mashumba, 18 W. Maluleke, 21 Seabi, 25 Sikhosana, 26 Nkili, 29 Mphambaniso, 50 Phali.
Golden Arrows: 32 Gumede, 20 Mathiane, 29 Sibisi, 5 Mzava, 3 Lunga, 16 Parusnath, 26 Phiri (Dube 46'), 12 Ndwandwe, 4 Venter, 41 Lamola, 18 Mutizwa (Sibeko 66').
Subs: 1 Mbaeva, 7 Matloga, 14 S. Dube, 17 Jooste, 22 Sibeko, 23 L Dube, 28 Bilankulu.