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.
Dewald Brevis has been ruled out of the Proteas' three-match ODI series in Pakistan, that starts in Faisalabad on Tuesday, after suffering a low-grade shoulder muscle strain.
Former India player Abhishek Nayar has been appointed head coach of the Kolkata Knight Riders in the Indian Premier League.
New Zealand veteran Kane Williamson has been signed by Indian Premier League franchise Lucknow Super Giants, albeit in a different role
In a major coup for the Big Bash League, Sydney Thunder have signed former India spinner Ravichandran Ashwin on a two-year deal.
