The goal came from defender Junaid Mashamaite.
It was just the second away win in the 2008/09 season for the Clever Boys, and coach Roger De Sa will be delighted to end the year safe in the knowledge that his team is well placed as far as challenging for the title is concerned.
In contrast, Swallows' Julio Leal will be frustrated at a second successive loss and the fact that his team seems to have an inability to win games at home; the Birds have won just one of the eight matches they have hosted in the Absa Premiership.
Wits dominated the early exchanges, with Sibusiso Mahlangu shooting just wide off the left hand upright in only the second minute after good build-up play by Sifiso Myeni.
Just before the midway point of the first half, Brazilian attacker Fabricio Rodrigues whipped a shot wide of Greg Etafia's goal from a free-kick on the edge of the 18-yard area, and on 24 minutes Mahlangu was desperately unlucky to see his effort rebound off the post.
Former Kaizer Chiefs midfielder Rene Richards tested Etafia with a shot from a free-kick in the 29th minute, but it was mere catching practice for the Nigerian.
Swallows, who had rarely troubled the Wits defence in the first half hour, finally got their attacking game going in the 36th minute, youngster Phumelele Bhengu heading wide of goal after meeting David Radebe's cross. Radebe himself was guilty of missing a good chance just before half time, shooting wide of stand-in keeper Darren Keet's goalposts.
Three minutes after the restart, Mahlangu's bad luck in front of goal continued when Greg Etafia made an excellent parrying save to keep out the midfielder's goalbound header.
However, less than ten minutes later, the Wits deservedly broke the deadlock when Mashamaite rose highest to convert Richards' free-kick and put the visitors 1-0 up.
On the hour mark Swallows' Cecil Oersen had the chance to test Keet from a set-piece, but the midfielder's shot was easy pickings for the goalkeeper. Nine minutes later Oersen blazed a shot wide of goal, much to the frustration of Leal on the sidelines.
On 77 minutes Keet made a fine reaction save to tip Radebe's header over his crossbar, this after the striker had managed to get on the end of Lefa Tsutsulupa's cross from a free-kick.
In the end Swallows' best efforts were simply not enough to prevent their third home loss this season, while Wits will be pleased to end the year near the top of the League standings.