Both sides scored five tries, but once the visitors sorted out their discipline, the away win always looked possible for the team coached by Jimmy Stonehouse.
The Lowvelders delivered a commanding second half performance after a very frustrating first half, which saw them trailing 21-10 and playing with 14 men twice in the opening 40.
The opening 20 minutes of the second half were decisive, as the Pumas scored some fantastic tries to push their lead out to 36-21 before the Lions found some late urgency, but their comeback effort came up short.
New Nation Pumas flyhalf Eddie Fouché had the first opportunity to get the scoreboard going five minutes in and made no mistake, following a Lions late tackle, but that was the only joy Stonehouse was enjoying in the next half hours.
No 8 Willie Engelbrecht send to the sin bin nine minutes in, and the hosts pounced.
The Sigma Lions opted for a scrum near the Pumas' line and using their numerical advantage, Rabz Maxwane ran in unopposed after a long pass from Jordan Hendrikse found the winger all on his own. Hendrikse did not mind the try in the corner and slotted the conversion with ease.
Fouché had another opportunity to the poles straight away, but the pivot pushed his effort to the right.
The visitors scored their first try 19 minutes in to reclaim the lead. With Engelbrecht back on the field, they attacked from behind their own 22m line with a number of delightful passes and offloaded freeing flying fullback Devon Williams on the outside. He dotted down, Fouche found his range again and suddenly Pumas were 10-7 up.
The Sigma Lions kept pressing though and soon had the Pumas under massive pressure near their own line. With their pack in control, they opted for attacking scrums as the Pumas buckled under pressure, conceding penalties and accumulating warnings from referee Marius van der Westhuizen. The referee decided enough was enough and awarded a penalty try to the home side after another collapsed scrum near the visitors' tryline.
That handed the lead back to the Lions after 25 minutes of play. A second yellow card - after seven penalties in a row - to captain Pieter Janse van Vuren had the visitors in deep trouble. The next Lions try, 32 minutes in, was almost inevitable as their pack, already in control, drove hooker PJ Botha over the line.
Hendrikse kicked another beauty from the touchline to stretch the lead to 21-10.
The rest of the half delivered a number of half chances to both teams, with the Sigma Lions no doubt rewarded for a better territorial effort and their 11-point lead at the break was fitting.
The second half saw a scorching start by the New Nation Pumas. They won three consecutive penalties through rolling mauls, each time kicking to the corner again and when former Valke lock Shane Kirkwood scored his first try for his new team and Fouche converted, the lead was cut back to three.
The Pumas regained the lead 50 minutes in. They again drove well from a line-out, forced the Lions on the backfoot, and then moved the ball to the wing where Etienne Taljaard cut through some weak defence to score.
Fouche converted and suddenly the visitors held a 24-21 lead. Lions lock FP Pelser was also sin-binned for collapsing a Pumas maul earlier in the move that led to the try.
That cost the hosts as the New Nation Pumas kicked to the corner from yet another Lions infringement and from the rough and tumble by his forwards, centre Erich Cronje found space in the opposing defence to score the bonus point try and a 29-21 lead.
That was extended to 36-21 from the restart. The New Nation Pumas attacked to the left, Matt More found space, Taljaard linked up with Williams and was on hand for the return pass to score under the posts. Fouché kicked the conversion.
Courtnall Skosan scored 64 minutes in to kick-start the Lions comeback. The winger came in from an angle after a strong Lions scrum and slipped through the gap created by decoy runners. Fred Zeilinga, who replaced Hendrikse earlier, kicked the conversion.
The Lions with newfound confidence and a rediscovered ability to hold onto possession started to ask serious questions to the Pumas defence, who had no answer. Prop Sti Sithole was driven over from an attacking line out and suddenly the lead was cut back to three with ten minutes to play.
Fouché missed a penalty to push the lead to six again and ease the nerves, but credit to his pack who controlled the last couple of minutes to secure the win.
Sigma Lions 33 (21) - Tries: Rabz Maxwane, Penalty try, PJ Botha, Courtnall Skosan, Sti Sithole. Conversions: Jordan Hendrikse (2), Fred Zeilinga (2).
New Nation Pumas 36 (10) - Tries: Devon Williams, Shane Kirkwood, Etienne Taljaard (2), Erich Cronje. Conversions: Eddie Fouché (4). Penalty goal: Fouché.