It didn't help Walsall's cause that they had experienced central defender Ian Roper sent off for a 65th minute foul on Darryl Duffy, which led to the penalty which gave Swansea their third goal.
But the visitors were superior in most departments, particularly in the centre of midfield which was ruled by Ferrie Bodde and Darren Pratley, while wideman Andy Robinson was always a dangerous raider, being rewarded with two goals.
Yet it was Walsall who had begun the brighter, inspired by teenager Ishmel Demontagnac.
Richard Money's men took the lead after just seven minutes when a slide-rule pass by Paul Hall found Martin Butler, who found the net with an angled shot from close range.
Walsall could have been further ahead two minutes later when a great left-footed shot by Demontagnac looked bound for the far corner, but keeper Dorus De Vries made an equally fine save.
In the 11th minute Swansea equalised when the home defence backed off Robinson, who sent in a low shot which deflected off full-back Rhys Weston and sent keeper Clayton Ince the wrong way.
Both sides could have scored further goals in an end-to-end match but it was an unlucky own goal by Ince which enabled Swansea to go ahead.
Clever striker Jason Scotland cut in and sent in a shot which hit a post and then rebounded over the line off Ince, with central defender Scott Dann vainly trying to clear.
Although Swansea always looked the better side, Walsall could have been level when a header by Dann was cleared off the line, but at the other end, both Dennis Lawrence and Duffey could have had goals for Swansea.
Although generally inferior to Swansea, Walsall stayed in it until the penalty incident and once Robinson had slotted home the spot-kick, there was only going to be one winner.
Even so, Walsall did have further chances, but it looks as though they may struggle where Swansea seemed to have what it takes to make a thrust for promotion.