The hosts went ahead in the 26th minute through a Edward Manqele strike, and it would prove to be the only score on the evening.
For Chippa, the three points could not be more timely as they surge up 28 points – now five ahead of the bottom three sides – in 13th spot on the log.
The Birds, however, now claim the favourites tag for the drop. The Dobsonville outfit remain on 22 points and are now last on the log, with Free State Stars ahead on goal difference and AmaZulu a point above.
Manqele made his presence felt early in the encounter. In the 12th minute the Chippa striker had a dip at goal but his effort was over the target.
Swallows replied straight back with a chance of their own. From a free kick Luyolo Nomandela sent the ball into the area, but the headed attempt by Rudi Isaacs was just over the crossbar.
William Twala for Chippa tried his luck just inside the quarter hour mark, but did not have the accuracy to trouble Sage Stephens in the Swallows goal.
Chippa were on the prowl again shortly after, with Andile Mbenyane coming in with the shot but he too could not keep his attempt down as the ball sailed into the stands.
The breakthrough came for the hosts halfway through the first period. Manqele was clinical in front of goal to open the scoring after the pass came in from Siyabulela Shai to make it 1-0 to Chippa.
With less than three minutes gone in the second period, Manqele had another chance but this time hit his attempt over the crossbar.
Just after the hour mark, Mbenyane had a chance of his own, but Stephens was alert to the danger as he parried the ball away from his goal.
Would you like to place a soccer bet? Click here to get started in 3 easy steps.