Siphelele Ntshangase was the hero for the hosts with a brace, with Thamsanqa Gabuza netting the other.
The match, a first leg CHAN 2016 qualifier, came after a week which was marred by player withdrawals and cancelled training sessions.
But, playing with a makeshift side that included three debutants in Wandisile Letlabika, Musa Nyatama and William Twala, the hosts had complete control, with birthday boy Itumeleng Khune making his first save in the 80th minute.
Predictably, playing against a side ranked 176th in the world, Bafana made all the running in the first half.
Ntshangase missed an early header from Gabuza’s cross, before Gift Motupa tested the goalkeeper with a powerful drive that was tipped over for a corner.
However, the goal did eventually come on 25 minutes through Gabuza. A short corner routine saw Marc van Heerden picking out the Orlando Pirates striker at the far-post, and he made no mistake from close range.
Mauritius had hardly caught their breath when Bafana scored a second. Some more enterprising play saw Mandla Masango slide a pass in to Ntshangase, who slotted through the keeper’s legs.
It was almost 3-0 shortly afterwards. Bafana had been finding space down the flanks throughout the half, and this time the build-up from the right found Masango, whose curling shot was tipped onto the upright.
However, the third goal was not far away, and again Ntshangase delievered, beating two defenders in the box and firing across the goalkeeper and into the bottom corner.
Bafana kept attacking after the break, with Ntshangase heading straight at the keeper from Gabuza’s cross, before Van Heerden had another free-kick tipped over.
Substitute Vuyisile Wana missed a great opportunity from right in front after being played in by Ntshangase, before another benchman, Bongi Ntuli, rounded the keeper but fired wide.
Mauritius had David Lengclume red-carded with 10 minutes to go, allowing even more chances for Bafana.
Ntshangase should have had his hat-trick, but first mis-kicked right in front of goals, then had a powerful shot cleared off the line, before heading onto the crossbar from right in front.
So Bafana will be confident of getting the job done in the return leg in Mauritius in two weeks’ time.
South Africa: Khune, Van Heerden, Gumede, Letlabika, Mngonyama, Motupa, Nyatama, Masango, Twala (Wana 67), Ntshangase, Gabuza (Ntuli 77)