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Two of Schoeman's tries came from driving mauls, while the other was from an attacking scrum when he was able to cross untouched after his tight five had shunted the Jaguares back and opened up the blind-side of the field.
Flyhalf Elton Jantjies added two conversions and two penalties for the Johannesburg-based side, who have made the Super Rugby final for the past three years.
With three penalties and a conversion, Jaguares flyhalf Joaquin Diaz Bonilla proved he could be a more than adequate replacement for Nicolas Sanchez in the wake of the Pumas veteran's move to Stade Francais.
Tighthead prop Santiago Medrano scored a first-half try for the home side, who continued to play an open and fast-game style but found it difficult to break down the Lions defence.
The Jaguares were also left to rue a missed opportunity to score in the 66th minute when Marcos Kremer lost the ball while over the line. After a sustained buildup of pressure Kremer had the ball stripped as he rolled to place it and the Lions cleared their own line and rampaged down field.
The visitors then used that field position to earn a penalty, which Jantjies slotted to give the Lions a 25-16 lead with little over 10 minutes remaining.
It was the first time in eight meetings between the sides that the team playing away from home had won the game.
The Jaguares made the playoffs last season and despite having a new coach in Gonzalo Quesada, captain in centre Jeronimo de la Fuente and making 10 additions to the squad, they still look likely to be in contention for the playoffs