The Rebels led 19-6 in the second period but the Jaguares fought back strongly in the final half an hour to secure a 25-22...
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Rob Vickers' late try secured a pulsating 35-30 win over Sale Sharks to propel Newcastle Falcons into the Premiership's top four.
Johan Goosen's return to rugby was spoiled by Munster, who engineered an impressive second-half turnaround at the Cheetahs in Pro14.
Beauden Barrett, Ben Lam and Ngani Laumape all scored tries as the Hurricanes defeated the Chiefs in Wellington.
It was a tough outing for La Rochelle at Montpellier, as Racing 92 defended resolutely in their Top 14 beating of Toulon.
Exeter Chiefs are assured of a top-four finish in the Premiership after scoring six tries in an emphatic win over Gloucester.
Castres, Stade Francais, Lyon, Bordeaux-Begles and Agen were the winners on a busy day of Top 14 action.
Scarlets picked up an impressive win over Glasgow Warriors to keep the pressure on Leinster, while Benetton, Cheetahs and Munster also won.
Ruthless Saracens scored nine tries in their latest thrashing of Northampton Saints, while London Irish eased to victory at Harlequins.
The Blues came closing to claiming a long-awaited win over the Chiefs, but a late penalty try denied them at Waikato Stadium.
Wasps looked to have done just enough to hang on against Sale, before Marland Yarde won the game for the Sharks in thrilling fashion.
Edinburgh were beaten at home by Ulster in the Pro14, while the Ospreys thumped Connacht in Swansea.
The Hurricanes were without Beauden Barrett against the Sharks but Ihaia West came good by kicking a game-winning conversion.
There will be new European Champions Cup winners this year after Leinster dumped Saracens out in Dublin.
Sam Whitelock and Jack Goodhue both scored tries as the Crusaders turned around a half-time deficit to beat the Lions in Johannesburg.
Clermont Auvergne suffered fresh European Champions Cup heartbreak, as Racing 92 powered through to the semi-finals.