Harry Mallinder, son of Northampton director of rugby Jim, produced the winning score as the Saints defeated Glasgow 19-15.
The victory at Franklin's Gardens keeps Northampton's hopes of progressing to the quarter-finals of the Champions Cup alive.
While Northampton's tally was made up of three tries, the visitors looked as though they would win the contest thanks to five well-taken penalties, but after a dramatic second half, Glasgow exited the competition despite a valiant effort.
The Pool 3 match was exciting for the neutrals, and even more so for Saints themselves, who know victory at bottom-placed Scarlets on Saturday could see them go through to the knockout stage of the competition.
Flanker Taimana Harrison crashed over for the home side early on, with JJ Hanrahan adding the extras with a clean strike.
Glasgow rallied their way back into the contest with two penalties, both kicked well by Scot, Finn Russell.
The first came as a result of debutant Sam Johnson being too strong for the Saints backline, while the second came as Northampton strayed offside.
In between the kicks, Tom Collins was forced off for the home side, but not before eight minutes of medical attention on the pitch following an accidental mid-air collision with Warriors' full-back Stuart Hogg.
Glasgow fought hard for a first-half turnaround, but it was not forthcoming as Saints held their backline to enter half-time with a 7-6 lead.
However, the visitors wasted no time in starting where they left off, earning a penalty inside two minutes of the restart. This time though, Russell saw his effort drift wide.
Northampton failed to learn from their mistakes, and Glasgow took the lead for the first time in the match, Russell atoning for his earlier misses.
That it seemed was just the kick the hosts needed, as Christian Day drove over for the second try of the match, restoring Northampton's lead.
The two sides remained just a penalty apart as the conversion was missed. But it seemed neither side could hold onto a lead, with Glasgow winning a scrum penalty, which was superbly taken by Russell to square things up at 12-12.
A period of play followed in which neither side could get their best rugby together, but Glasgow received their second scrum penalty of the day with less than ten minutes left on the clock.
Hogg hit home the three points, handing the away side the lead once more. Glasgow were then forced to play the final six minutes with 14 men, as Tim Swanson was sin-binned for an offence in the maul.
And that paid dividends for Northampton, who scored their third try of the day in the dying moments as Harry Mallinder got over the line after a lucky bounce in the build-up.
As the home fans celebrated and the visitors despaired, Stephen Myler converted to cap off a wonderful match.
Tries: Harrison, Day, Mallinder
Cons: Hanrahan, Myler
Pens: Russell 4, Hogg
Yellow Card: Swinson
Northampton Saints: 15 Ben Foden, 14 Tom Collins, 13 George Pisi, 12 Luther Burrell, 11 George North, 10 JJ Hanrahan, 9 Lee Dickson (c), 8 Teimana Harrison, 7 Tom Wood, 6 Jamie Gibson, 5 Christian Day, 4 Courtney Lawes, 3 Paul Hill, 2 Dylan Hartley, 1 Alex Waller
Replacements: 16 Mikey Haywood, 17 Ethan Waller, 18 Gareth Denman, 19 Michael Paterson, 20 Jon Fisher, 21 Tom Kessell, 22 Stephen Myler, 23 Harry Mallinder
Glasgow Warriors: 15 Stuart Hogg, 14 Lee Jones, 13 Alex Dunbar, 12 Sam Johnson, 11 Sean Lamont, 10 Finn Russell, 9 Ali Price, 8 Adam Ashe, 7 Chris Fusaro, 6 Ryan Wilson, 5 Jonny Gray (c), 4 Leone Nakarawa, 3 Sila Puafisi, 2 Pat MacArthur, 1 Gordon Reid
Replacements: 16 Shalva Mamukashvili, 17 Alex Allan, 18 Zander Fagerson, 19 Tim Swinson, 20 Simone Favaro, 21 Grayson Hart, 22 Duncan Weir, 23 Taqele Naiyaravoro
Referee: Romain Poite (France)
Assistant Referees: Cyril Lafon (France), Stéphane Boyer (France)
TMO: Philippe Bonhoure (France)