Tanners outplayed their hosts from start to finish and the final result could have been a lot more emphatic, had it not been for some heroic goalkeeping from Swans’ custodian Mo Maan and his replacement Dane Buss.
Boss Richard Brady gave a debut to Daniel Johnson at left back and the young defender played an important part in the visitors’ opening goal after 15 minutes.
He launched a probing free kick deep into the Swans’ six yard box and Ian Draycott rose above his marker to head home.
Leatherhead doubled their lead three minutes later through a bizarre own goal, when leading scorer Tom Bradbrook was beaten to the ball by Swans defender John Clark, who powered it into the net from 20 yards.
Bradbrook assisted in Leatherhead’s third goal after 37 minutes - the Leatherhead striker’s fierce drive was only half-blocked by Maan and Draycott was well placed to score on the follow up.
Bradbrook was a whisker away from adding Leatherhead’s fourth on the stroke of half-time, with another long range effort scraping the top of the bar.
Tanners did not have much longer to wait, however, as another Bradbrook thunderbolt was cleared off the line after 52 minutes, only for Paul Semakula to latch onto the loose ball and nudge the ball home from close range.
Swans' demolition was completed with a fifth goal after 64 minutes when Tanners sub Mohamed Eisa fed a ball down the left channel to Draycott, who cleverly chipped it across the width of the goal for Bradbrook to head home at the far post.
Maan, who had played through much of the match in apparent discomfort with a wrist injury, was replaced in goal for the final 25 minutes by substitute keeper Buss, but some fine goalkeeping meant Tanners were unable to add further to their tally.
Leatherhead: Deren Ibrahim, Ryan Mahal, Daniel Johnson, Tom Parkinson, Jamie Coyle, Jerry Nnamani (Ryan Cooper 74), Kev Terry (Mohamed Eisa 57), Darren Smith, Tom Bradbrook, Ian Draycott (Jake Hobbs 74), Paul Semakula.
Unused sub: Mikey Dalton