The Buccaneers made four changes to their starting eleven and were eager to bounce back after their narrow loss to Kaizer Chiefs last weekend.
Saleng opened the scoring for Pirates in the 6th minute with a cheeky back-heel at the near post from Kabelo Dlamini's low cross.
Although both teams struggled to create clear chances, Saleng came close to doubling the lead with a volleyed shot that missed the net due to poor communication between Swallows' goalkeeper Thakasani Mbanjwa and his defence.
Tawanda Macheke thought he had equalized for Swallows with a shot from a loose ball after a cross in the box, but the goal was disallowed for offside.
The second half started well for Pirates as they doubled their lead just two minutes in when Terrence Dzvkumanja's shot deflected off Mthokozisi Shwabule from a cross by Saleng to make it 2-0.
Saleng completed his brace in the 60th minute with a tap-in from a cross by Dlamini.
Swallows committed more players forward in search of a goal. They were rewarded in the 76th minute when Shwabule pulled a goal back with a first-time shot in the box from Tlakusani Mthethwa's cross.
Pirates coach Jose Riveiro made a double substitution with 16 minutes remaining, bringing on Kermit Erasmus and Marou Souaibou in place of Dlamini and Thembinkosi Lorch.
However, it was Saleng who had the final say in stoppage time as he completed his hat-trick by racing clear on goal and firing a low strike past Mbanjwa.
The 4-1 victory sees Pirates move within two points of second-placed SuperSport United in third place on the log, while Swallows find themselves in 14th position.