Gouws Prinsloo's match-winning conversion broke Pumas hearts in the first-leg of the Currie Cup relegation/promotion clash.
The visitors had raced into a surprising 13-0 lead which they held at half-time as Griquas persistently rejected chances to kick at goal.
A double blow of tries for the hosts took them into a 14-13 lead in the second half but the Pumas looked to have it won after two penalties from replacement JC Roos.
But a stunning result wasn't to be as Marnus Schoeman crossed with only one minute to spare, with Prinsloo adding the extras for the win.
Pumas fly-half Carl Bezuidenhout added two penalties in the first ten minutes, the second from 50m, to put the First Division side into a promising lead.
Wilmaure Louw then doubled the visitors' excellent start with a try in the 23rd minute, Bezuidenhout converting to put the Pumas 13-0 ahead and silencing the home crowd.
A dominant Pumas scrum caused persistent problems throughout the first half and it yielded the first try after pressuring Griquas near to their own line, Louw pouncing on stolen possession.
Griquas came close to grabbing a foothold in the match but were denied by the TMO for being held up, leaving them trailing 13-0 at half-time as the Pumas benefited from greater continuity and execution in their play against the Premier Division side.
The home side's persistent option to kick for the corner rather than for points continued to cost them, rejecting five opportunities to go for goal but still remaining scoreless after 45 minutes.
Blindside flanker Schoeman came agonisingly close for Griquas again when he crashed over the line, but the effort was ruled out by the TMO for accidental obstruction.
Griquas' first-half scrummaging woes gradually began to swing in their favour after the interval as they won two scrums against the head, but a penalty for holding on near the line to continue their ongoing frustrations.
The Pumas resistance couldn't last, as Griquas scored two tries in four minutes through replacement Carel Greeff and Jean Stemmet to swing the tide in the hosts' favour.
It didn't last long. Replacement Roos slotted a 65th minute penalty to put the Pumas back in the lead. His second effort in the 73rd minute gave the Pumas a five-point lead.
With the Pumas targeting a famous win in their sights, their hopes were then dashed by Schoeman's 79th minute heartbreaker as he crashed over in the corner to level the scores.
The responsibility rested on Prinsloo to land the match-winning conversion from out wide, which he did with aplomb as the hosts snatched victory in the final moments.
Tries: Greeff, Stemmet, M.Schoeman
Con: Prinsloo 3
Pens: Bezuidenhout 2, Roos
Griquas: 15 Gouws Prinsloo, 14 Willie le Roux, 13 Jean Stemmet, 12 Howard Mnisi, 11 Rocco Jansen, 10 Francois Brummer, 9 Marnus Hugo, 8 Burger Schoeman, 7 RJ Liebenberg, 6 Marnus Schoeman, 5 Jaco Nepgen, 4 Rynard Landman, 3 Lourens Adriaanse, 2 Ryno Barnes (c), 1 Steph Roberts.
Replacements: 16 Matt Dobson, 17 Janro van Niekerk, 18 Patrick O'Brein, 19 Carel Greeff, 20 Jacques Coetzee, 21 JP Nel, 22 Nico Scheepers.
Pumas: 15 Coenie van Wyk, 14 JW Bell, 13 Wilmaure Louw, 12 Stefan Watermeyer, 11 Rosco Speckman, 10 Carl Bezuidenhout, 9 Francois de Klerk, 8 RW Kember, 7 Renaldo Bothma, 6 Corne Steenkamp (captain), 5 Eduan Van Der Walt, 4 Rudi Matthee, 3 Ivann Espag, 2 Frank Herne, 1 CornÃ© Fourie.
Replacements: 16 Francois du Toit, 17 Vincent Koch, 18 De-Jay Terblanche, 19 Lubabalo Mtyanda, 20, Uzair Cassiem, 21 JC Roos, 22 Dewald Pretorius.
Referee: Jonathan Kaplan
Assistant referees: Lourens van der Merwe, Francois de Bruin
Television match official: Johan Greeff