The 21-year-old Brevis, who came into the Chennai squad mid-season as an injury replacement, struck four sixes in his knock as the men in yellow were restricted to 154 all out.
The young South African, who came in at number five, received no real support with the next best contributor Ayush Mhatre who scored 30 while Deepak Hooda made 22 late in the innings.
Brevis' innings was ended 13th over due to a brilliant catch taken on boundary by Sri Lanka international Kamindu Mendis.
Mendis then starred with the bat as he was unbeaten on 32 to guide the Sunrisers to victory with eight balls to spare after they were wobbling at 90-4.
The Super Kings remain at the foot of the IPL standings having only won two of their nine matches so far this season while the Sunrisers have one more win and are two points better off.
Lhuan-dre Pretorius, Dewald Brevis and Codi Yusuf will all make their Test debuts for the Proteas against Zimbabwe in Bulawayo on Saturday, stand-in captain Keshav Mahraj has confirmed.
Lhuan-dre Pretorius, Lesego Senokwane, Dewald Brevis, Prenelan Subrayen and Codi Yusuf could make their Test debuts for the Proteas in the two-match series in Zimbabwe that starts on 28 June.
Proteas coach Shukri Conrad has selected five uncapped players in a 16-man squad for the two-match Test series in Zimbabwe that will start on 28 June at the Queens Sports Club in Bulawayo.
Royal Challengers Bengaluru sealed their maiden Indian Premier League (IPL) title after beating Punjab Kings by six runs in the final at Ahmedabad on Tuesday.
