In a combative final, Wits scored first through Jabulani Shongwe, but Bucs hit back after the interval via efforts from Man of the Match Erasmus and ex-Students ace Sifiso Myeni at Moses Mabhida Stadium.
The Buccaneers were under heavy pressure to deliver after stumbling at the last hurdle of the CAF Champions League, the Telkom Knockout and MTN8 earlier in the campaign.
Vladimir Vermezovic's charges started the tie brightly, as Erasmus's shot in the box nearly snuck under goalkeeper Moeneeb Josephs as early as the opening minute.
Soon after, Pirates had a decent penalty shout rejected by referee Zolile Mthetho amid claims S'boniso Gumede handled in the area during a goal-mouth scramble.
The Clever Boys, though, drew first blood in the 26th minute, as Shongwe thundered the ball into the roof of the net from close range following good work from Sthembiso Ngcobo.
Gavin Hunt's men finished the stanza promisingly, although they lost the services of Calvin Kadi just before the recess as he damaged his knee when making a tackle on Happy Jele.
Wits threatened early into the second period, as Ngcobo's ferocious free-kick from range, following a foul by Thandani Ntshumayelo on Sibusiso Vilakazi, was unconvincingly kept out by Senzo Meyiwa.
The Sea Robbers, however, drew level in the 52nd minute, as Erasmus converted Oupa Manyisa's cut-back from the right with the help of a deflection from 14 yards.
At the other end, Meyiwa did well to foil a Ngcobo flick-on following a long throw-in by Phumlani Ntshangase.
Pirates then took the lead in the 63rd minute, as Myeni poked the ball home from a few yards out, with Manyisa once again providing the assist.
Erasmus made it 3-1, and effectively ended the contest, in the 72nd minute with a clinical strike in the box.
Wits, to their credit, nearly reduced the deficit in optional time, but Meyiwa made a brilliant stop to deny a bullet header from substitute Ryan Chapman.