Morgan struck a solo goal to seal the points for Aldershot after his side had levelled the scores from the penalty spot via the boot of Scott Donnelly.
Donnelly netted after referee Fred Graham gave a penalty to the home side for a foul by Paul Ro
dgers. Cobblers keeper Chris Dunn saved the initial spot kick but the official spotted an infringement and Donnelly converted the re-take.
The Cobblers had dominated the first half and deservedly took the lead with Luke Guttridge the man on the score sheet. The talented number four beat the offside trap to slot in after good work from Adebayo Akinfenwa and in truth the away side could have gone in at the break with more than one goal to their name.
Ian Sampson sprang what many may have considered a surprise prior to kick-off as he named Akinfenwa in the starting line-up and the big front man caused Aldershot problems almost immediately.
His link-up work with Guttridge on the right side was really troubling the home side and that combination came to fruition on 17 minutes as Akinfenwa slid the ball through for his teammate to slide the ball in.
The lead was no more than the Cobblers deserved after a bright start but Aldershot began to come back into it and their star man Louis Soares was gifted an effort from the edge of the area but he hit it just wide.
Home hitman Morgan then got in on goal but he shot wildly over from inside the area with just Dunn to beat.
Cobblers sensed that they needed to get a foothold in the game once again and Guttridge was denied by Jaimez-Ruiz after another good pass from Akinfenwa.
Andy Holt also had a chance to double the away advantage but he headed narrowly over with 10 minutes to go before half-time.
Aldershot made a double substitution during the interval and they attempted to exert some pressure early on but their shots were all high wide and not so handsome. Scott Donnelly had the best effort in but his long range effort failed to test Dunn.
The keeper was forced into action on the 66 minute mark, though, as he pulled off a sensational save to deny Halls' 25 yard curling effort.
The Cobblers were struggling to get any sort of possession and their opponents had a succession of corners before referee Graham awarded a highly contentious penalty to the Shots.
Dunn made a brilliant low save from Donnelly's spot kick, which was given for a foul by Rodgers on Anthony Charles, but a re-take was ordered and the midfielder made no mistake at the second attempt.
The Cobblers players were losing their head with the man in black and Ian Sampson was raging on the touchline but in their angst the away side created a chance. Holt cut in from the left and stung the palms of the keeper.
Things were to get worse for Sampson's unlucky side on the 90 minute mark as Shots striker Morgan cut inside from the left and beat Dunn to win the game for the hosts.
ALDERSHOT: Jaimez-Ruiz, Herd, Straker (Grant 45), Blackburn, Charles, Soares, Chalmers (Halls 45), Morgan, Donnelly, Hudson (Harding 75), Sandell. Subs not used: Winfield, Hopkinson, Connolly, Masters.
COBBLERS: Dunn, Rodgers, Guttridge (Dyer 84) , Walker, Guinan, Akinfenwa (Mulligan 50), Holt, Gilligan, McCready (Hinton 90), Gilbert, Kanyuka. Subs not used: Brown, Curtis, Jacobs, McKay.
