Quilmes defeated Gimnasia 2-0 on Sunday to hand the former leaders their first defeat in seven games and both Estudiantes and River Plate took advantage to leapfrog the La Plata-based club.
Estudiantes, who are also from La Plata, had moved into first position in the standings when they cruised past San Lorenzo 3-0 on Saturday and held onto top spot after their arch-rivals lost, but River's victory in Sunday's late match saw the Buenos Aires-based giants edge ahead by two points with just one round to play in the second half of the Primera Division season.
Gabriel Mercado and Teofilo Gutierrez scored in the second half for River, as they rose to 34 points, ahead of Estudiantes (32) and Gimnasia (31), while Boca Juniors (29) trumped Lanus 3-1 to claim fourth in the table ahead of Godoy Cruz on goal difference.
The winner of the Torneo Final will play Torneo Inicial champions San Lorenzo in a one-off Super Final at a neutral venue.
At Argentinos Juniors' Estadio Diego Armando Maradona, River had to wait until after the break to open the scoring with Mercado poking the ball home in the 69th minute after the hosts failed to clear a free-kick from their penalty area.
Gutierrez capped off the vital win for the visitors in the 78th minute, taking advantage of a turnover caused by Fernando Cavenaghi, and shooting between the goalkeeper's legs to score.
In Quilmes, an own goal from Gimnasia's Fernando Monetti five minutes into the second half and Lucas Perez Godoy's stoppage-time strike saw the home side triumph.
River will wrap up the Torneo Final title with a win against Quilmes on the final day of the regular season next Sunday, while Estudiantes, Gimnasia, Boca and Godoy Cruz will need other results to go their way if they are to reel in the leaders.
Franco Jara was the hero for Estudiantes on Saturday, scoring a brace against San Lorenzo, who conceded twice in the opening 13 minutes.
Godoy Cruz lost 3-1 to Olimpo on Friday to leave them rank outsiders to claim the title.
Colon lost 2-0 at Velez Sarsfield as they strive to avoid relegation.
In the Primera Division, the bottom team across the Inicial and Final campaigns are relegated, as are the two clubs with the worst points average over the past three seasons.
Argentinos Juniors and All Boys have already been relegated this season and Colon, with a points-per-game average of 1.23, dropped into the third relegation spot on Saturday behind Atletico de Rafaela, who drew 1-1 with Tigre, but have the same average as Colon.
Colon host Olimpo on the final day of the Torneo Final campaign, while Atletico de Rafaela travel to Arsenal.
In other results, Newell's Old Boys defeated All Boys 4-2, and Racing Club and Belgrano were held to scoreless draws by Rosario Central and Arsenal respectively.
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