McLeod struck in the 45th and 69th minutes and completed his trio with the last goal four minutes from time to take his season's tally up to seven.
Lee Trundle weighed in with a brace and there was one apiece for Adebayo Akinfenwa and Leon Britton.
Kenny Jackett was forced into one change as Owain Tudur Jones had not recovered from an injury picked up playing for Wales' under-21s in Poland. His place was taken by Marcus Bean on loan for a second time from Queens Park Rangers.
The Robins packed midfield and it stifled the Swans until the final minute of the first half when a vicious corner by McLeod swerved inside the near post while Bristol keeper Steve Phillips had one eye on Akinfenwa.
After the break the Swans cut loose and the young Robins defence was cut to pieces.
Akinfenwa evaded a couple of half-hearted challengers as he strode down the middle before calmly slotting into the corner of the net.
Seven minutes later Trundle put the game beyond the sad visitors by slotting home a spot-kick awarded after skipper Roberto Martinez had been pulled back.
With the Robins defence now in complete disarray, it was no surprise when McLeod let fly a 30-yard special that hit the back of the net before Phillips could move.
By now the under pressure Robins manager Brian Tinnion had thrown on half-fit Marcus Stewart and Scott Murray and at least Stewart was able to show his pedigree by holding on to the ball a little.
The tide kept moving towards the Bristol end and Britton raced through to beat Phillips with a delightful shot from outside the area.
Still the Swans weren't finished and McLeod bagged a deserved hat-trick with his side's seventh goal when he beat the offside trap to fire in from close range.
Wales under-21 cap David Cotterill scored a consolation goal for the Robins when his shot took a slight deflection and in the last minute Swansea's Kevin Austin was dismissed after an incident in the home goalmouth.
That couldn't take away a fantastic performance by the Swans who will surely now be recognised as genuine promotion contenders.