Daine Klate scored a brace for the Students, but it proved mere consolations.
As early as the eighth minute, Modise produced some flair as he got better of the ex-Brazilian Jabulani Shongwe with a ‘shibobo’, with the latter receiving a yellow card.
Bongani Zungu did brilliantly to clear Klate’s header off the line on 17 minutes after Siyabonga Nhlapo’s cross had taken Mweene out of the equation, but it was the hosts who grabbed the lead three minutes later through Malajila, who received a pass from Billiat, cut inside and beat Moeneeb Josephs.
Wits saw Klate’s free-kick sail over the bar and a penalty appeal for handball against Mzi Mashaba waived away as the halftime whistle blew.
The Students hit the ground running at the start of the second half, with Mweene parrying Klate’s close-range volley before Buhle Mkhawanazi hit the woodwork from the follow-up.
Josephs produced a memorable save to keep out Mogakolodi Ngele’s long-range thunderbolt before Wits leveled just past the hour-mark – Klate with a fine diving header after the ball had flicked off Rama Mphahlele’s head.
As time was running out and both sides were seemingly settling for a draw, the Brazilians pushed forward and were rewarded when Malajila found the back of the net after a goalmouth scramble.
A few seconds later Elias Pelembe’s effort hit the posts, before Billiat produced a brilliant bit of skill to take down a high-ball, beat a defender and then slot under Josephs.
A minute later and it was 4-1 as Modise curled home a beauty from the edge of the area, with Klate rounding off the scoring in time added on from Pelembe’s pass.