Maties opened the scoring through winger Rynhardt van der Linden after sustained early pressure, with flyhalf Christiaan van Heerden Smith adding a penalty.
UJ responded through a rolling maul finished by Kamo Molefe, before captain Thabang Mphafi extended their advantage to give the visitors an eight-point half-time lead.
But the hosts took full control after the break.
Centre CJ Marx sparked the turnaround, with hooker CJ Erasmus powering over from close range to edge Maties in front. Mckyle Volmink dotted down in the corner before centre Ryan Manuel added a classy finish.
Captain Ezekiel Ngobeni capped a dominant final quarter with a powerful try to complete the win, with Marx named Man of the Match.
WATCH: ‘Boogieman’ strikes fear
In Potchefstroom, the NWU Eagles made it two wins from two with a commanding 63-15 triumph over Emeries. Wing Therlow Prins starred with a hat-trick.
UCT bounced back from their opening-round defeat to Tuk by demolishing CUT 83-34 in a 17-try spectacle at the Green Mile.
In Bloemfontein, Tuks claimed a hard-earned 38-22 win over Shimlas at a rain-soaked Shimla Park, with Divan du Toit’s tactical kicking proving decisive.
Round 2 results
Maties 39 UJ 19
NWU 63 Emeries 15
UCT 83 CUT 34
Tuks 38 Shimlas 22
Round 3 fixtures
Monday, 2 March
UJ vs NWU (4:45pm, SuperSport)
CUT vs Shimlas (7pm, SuperSport)
Tuks vs Maties (7pm)
Emeries vs UCT (7pm)