While Cruzeiro maintained their strong start to the Copa Libertadores group stage with a 3-0 win over Mineros de Guayana, River had to settle for their fourth consecutive stalemate in South America's premier club competition, drawing 2-2.
Colombian striker Teofilo Gutierrez inspired River's recovery mission after they trailed by two goals with four minutes remaining, scoring the Argentine visitors' first goal and setting up the equaliser.
After Egidio Arevalo and Damian Alvarez scored either side of half-time to put Tigres in control, a defensive mix-up in the 87th minute saw River striker Rodrigo Mora one-on-one with the goalkeeper and although the Uruguayan's shot was saved, Gutierrez tucked home the rebound.
In the 90th minute, Gutierrez received a pass on the right side of the penalty area and his cross was powerfully volleyed into the net by Mora.
River had Gabriel Mercado sent off in second-half stoppage time but the draw would have been little consolation for Marcelo Gallardo's men, as it left them two points behind second-placed Juan Aurich in Group Six with one game left.
Tigres (11 points) remain unbeaten and top of the Group Six standings, while Juan Aurich (six) remain second ahead of third-placed River and bottom club San Jose (both four).
River must beat San Jose in Buenos Aires on the final matchday, and hope Juan Aurich fail to win at home against Tigres, if they are to reach the knockout stages.
In Belo Horizonte, Cruzeiro struck twice in the opening quarter of an hour to set up their win over Venezuela's Mineros.
The victory took Cruzeiro to the top of Group Three with Giorgian De Arrascaeta, Leandro Damiao and Henrique scoring at the Estadio Governador Magalhaes Pinto.
Cruzeiro (eight points) lead Club Universitario by two points in Group Three, with Huracan (four) and Mineros (one) trailing.
Universitario held Huracan to a 1-1 draw in Argentina, while Deportivo Tachira and Sporting Cristal completed a goalless stalemate.
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