The Reds squandered a promising lead in Argentina as the Jaguares claimed their second win of the season.
Julian Montoya's hat-trick propelled the Jaguares to victory over the winless Reds, while the Stormers pipped the Lions late in a Super Rugby thriller.
Looking for a lift after successive losses to start the season, the Reds began well in Buenos Aires on Saturday before succumbing to a second-half onslaught in an eventual 43-27 defeat.
Tate McDermott and Liam Wright crossed in the opening 20 minutes and Chris Feauai-Sautia grabbed a first-half double to hand Brad Thorn's men a 12-point advantage at the interval.
Argentina hooker Montoya scored the home side's sole first-half try and then led the second-half turnaround, touching down twice more amid a dominant 30-minute, five-try burst.
Emiliano Boffelli, Santiago Socino and Tomas Cubelli also crossed and Domingo Miotti contributed 11 points from the tee to ensure the Jaguares returned to winning ways after last weekend's loss to the Hurricanes.
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The undefeated Stormers needed a last-gasp Ruhan Nel try to snatch a heart-stopping 33-30 win over the Lions in Johannesburg.
The South African Conference leaders, who were ahead 26-15 early in the second half, gave up 15 unanswered points before Nel received Sergeal Petersen's brilliant offload and scored more than 90 seconds after the siren had sounded.
The Lions had taken the lead through Dan Kriel in the 73rd minute, but the late heartbreak left them with a solitary victory from the first three rounds.