The Valiants got their first sight of goal after 11 minutes when the ball fell kindly inside the area for Leon Constantine, but his ten-yard shot lacked any direction and flew into the stand behind.
Martin Foyle's men were let off the hook in the 16th minute when Leon Britton's deflected shot fell into the path of Rory Fallon but the striker failed to find the slight touch it needed.
Colin Miles' game was cut short in the 22nd minute when he was forced to retire through injury and he was replaced by the more mobile Jason Talbot.
After growing in confidence for much of the half, Paul Harsley summed up his side's frustrations when he hit a 35-yard half-volley that bounced wickedly in front of Andy Oakes but couldn't find the net.
Swansea almost earned themselves a dream start to the second half when Britton's winding run down the right flank produced a cross for Andy Robinson who should have done better than just firing wildly over the top.
The left-back position seemed to be jinxed on this particular afternoon as Talbot added himself to the Vale injury list after coming off worse in a physical challenge.
The Swans found themselves on the back foot as the game entered the latter stages with substitute Joe Cardle firing a stinging shot narrowly past the goalkeeper's right-hand post.
Britton let the crowd know that Swansea were still very much in the game when he hit a pot shot out of nothing in the 85th minute that Mark Goodlad dealt with comfortably.
After being almost anonymous for most of the match, Lee Trundle showed a flash of brilliance as he beat Richard Walker and fired a well placed shot into Goodlad's bottom left corner in the 90th minute.
Trundle hammered the nail into Port Vale's coffin in stoppage time when his trickery unlocked the defence once more before he supplied substitute Thomas Butler with a pass for a tap-in goal.