The 19-year-old nipped in to take advantage when defender Mike Williams made a hash of a back header to his goalkeeper Michael Ingham, leaving the way open for the Cobblers player to chip the ball into a gaping net.
Wrexham had the better of the early play and youngster Mark Jones might have scored early on when he ran from the half way line, skipped past two tackles and fired a low shot that Lee Harper went down to save.
The Wrexham teenager might have done better to pass to strikers Sam Williams and Matt Derbyshire who were waiting unmarked at the other side of the box.
Northampton came back into the game and from a David Hunt free-kick, Scott McGleish glanced a header narrowly past the far post.
Again, when Eoin Jess provided the centre, Andy Kirk cut in and saw Ingham making a brave diving save.
From another Jess cross, McGleish just failed to connect at the back post.
Wrexham defender Shaun Pejic had to clear off the line from Jason Crowe after a quickly taken free-kick nearly caught Wrexham off guard, and Danny Williams completed the clearance.
Again Ingham had to dive at the feet of McGleish when Kirk crossed and Williams deflected the shot towards his own goal.
From a Hunt corner the lively McGleish shot too high and the hard working Jamie Hand might have capped a star performance with a goal, but fired too high.
Gilligan scored early in the second half and changed the game, allowing the Cobblers to sit on their lead and let Wrexham do the running.
Pejic headed over from a Matt Crowell corner and then Crowell created another opening from a free-kick, before Dennis Lawrence headed down in the box for Sam Williams to see his shot saved on the line.
With time running out the hard working Jim Whitley tried a 25-yard shot that went straight into the arms of keeper Harper, making one of his few saves in an even game.