Sweswe scored his first ever goal in the PSL, but the glory of the Kaizer Chiefs win fell on the shoulders of their goalkeeper Bartman, who produced a number of quality saves and was rightly awarded Man of the Match.
The Brazilians dominated, controlling possession and having the majority of shots on goal. But after some stubborn defence from the Phefeni Glamour Boys and brilliant goalkeeping from Bartman, Chiefs were able to hold on for the win and move to 24 points on the log, joint third spot.
Chiefs did start the better of the two teams when they took the lead in the 12th minute, after Sweswe got onto the end of a superbly weighted right-wing free-kick from Siphiwe Tshabalala.
The Amakhosi defender headed home past a stranded Wayne Sandilands to make it 1-0.
After going behind, the Brazilians threw everything forward in attack, but found a formidable Bartman in their way.
In the 18th minute Nyasha Mushekwi drove through the middle of the Chiefs defence and found himself with only the keeper to beat, but Bartman produced a good one-on-one save.
Nine minutes later Themba Zwane pulled a pass back for Elias Pelembe on the edge of the 18-yard box, but his shot was superbly saved by Bartman diving low to his right.
In the 32nd minute Downs were denied by the woodwork, as a 25-yard shot from Teko Modise had the beating of Bartman but struck the left post and bounced away from danger.
The second half was more of the same as Chiefs defended for all their worth, while Sundowns pushed everyone forward.
Still, the Brazilians' only real chance of the half came in the 59th minute, and Bartman was there to deny them again.
The Amakhosi goalie produced another great double save, first to deny Siyanda Xulu from close range after a goalmouth scramble, and then punching the ball away as it pinballed around six-yard box.
In the end, the three points probably kept Chiefs coach Vladimir Vermezovic in a job.