Swallows came from two goals down to beat relegation candidates Baroka in a crucial DStv Premiership match at Dobsonville Stadium on Sunday.
The visitors opened the scoring in the 20th minute via a Sekela Sithole free-kick.
Richard Mbulu increased the lead early in the second half for Bakgaga.
But a brace by Mwape Musonda in the space of four minutes gave the home side some hope as they made it 2-2.
Substitute Musa Nyatama sealed the victory for the Dube Birds with four minutes to go.
Swallows jumped to 14th position with 23 points while Baroka remain bottom with 18 points.
