After a 0-0 draw following 90 minutes in Abidjan, Williams saved spot kicks from Chancel Mbemba and Meschack Elia to give Bafana Bafana the bronze medal in the African Cup of Nations [AFCON] in Ivory Coast.
Before Elia had his kick saved, Siyanda Xulu converted to give South Africa what proved the decisive lead in the shootout.
Williams saved four shootout kicks last weekend to help South Africa get past Cape Verde after a goalless quarter-final.
DR Congo will regret many missed chances during regular time in a lively match while South Africa maintained a perfect record in third-place play-offs having beaten Tunisia on penalties 24 years ago.
South Africa made three changes to the team beaten in a penalty shootout by Nigeria after an incident-packed semi-final three days ago.
Nkosinathi Sibisi, Thapelo Morena and Mihlali Mayambela came in for suspended Grant Kekana and injured duo Mothobi Mvala and Percy Tau.
DR Congo retained only two of the side that lost to hosts Ivory Coast in the other semi-final — captain and centre-back Mbemba and midfielder Samuel Moutoussamy.
But eight of the nine who were dropped sat on the bench, leaving French coach Sebastien Desabre with multiple options should he wish to make changes.
Threatening
Although the Congolese had less of the ball in the opening half at Stade Felix Houphouet-Boigny in the Ivorian economic capital, they were the more threatening team in the attacking third.
Physically imposing Silas Mvumpa came close to breaking the deadlock after just eight minutes, but as he tried to round Williams in the area, the goalkeeper snatched the ball.
Simon Banza worked his way into a dangerous position close to the South African goal midway through the half, only to deliver a weak shot that posed no danger.
Despite some neat build-up play, it took South Africa 43 minutes to get a shot on target, and the effort from Mayambela went straight to goalkeeper Dimitry Bertaud.
As the match reached the mid point of the second half, Congo continued to look the side more likely to break the deadlock.
When Williams fumbled the ball and lost possession, the ball went across the goalmouth and Silas fired wide when he should at least have hit the target.
So should Mbemba, who had ventured forward for a free-kick, but he blazed over when the ball fell invitingly into his path close to goal. Substitute Fiston Mayele also wasted a chance.
A captivating tournament concludes on Sunday in another Abidjan stadium with the Ivory Coast facing Nigeria in the final with a seven million dollar prize on the line.
The countries met at the group stage last month in the same venue and the Super Eagles won 1-0 thanks to a William Troost-Ekong penalty.
