Uchuari earned the penalty when River Plate's central defender German Pezzella clipped his ankle just after the hour mark and LDU's 19-year-old playmaker stepped up to convert the spot kick and wrap up victory at the Estadio Federativo Reina del Cisne.
In a tight and often feisty encounter in Loja, Uchuari led the way for the hosts, starting the move that led to his team's opening goal and then scoring the winner.
The victory on Thursday means LDU will head to Argentina next week with plenty of confidence, although River Plate will remain hopeful of reaching the quarter-finals after Osmar Ferreyra's away goal.
LDU took the lead just after the half hour mark when Uchuari took a free-kick on the left wing, and his squared ball to found Dixon Arroyo, whose shot was deflected in by captain Pedro Larrea.
The Argentine visitors equalised in the 59th minute when Ferreyra finished off Manuel Lanzini's good lead-up work but LDU struck back only seven minutes later when Uchuari scored from the spot.
While Pezzella was furious to have been penalised for a trip on LDU's teenage star, the referee had no hesitation pointing to the spot or yellow-carding the River Plate defender.
Uchuari slotted his penalty into the top-right corner as River Plate goalkeeper Marcelo Barovero dived the wrong way and LDU were on track for victory.
In just their second appearance in a South American continental club competition, LDU will hope to go one better than in the 2012 Copa Sudamericana, when they were eliminated by Sao Paulo of Brazil in the round-of-16.
In other round-of-16 first legs, Argentina's Lanus thrashed visiting Universidad de Chile 4-0 thanks to a brace from Lucas Melano, while another Argentine club, Velez Sarsfield won 2-1 away to La Equidad of Colombia.
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