Trailing 2-1 heading into the 95th minute at the Estadio Ciudad de Lanus-Nestor Diaz Perez on Friday, midfielder Diego Gonzalez side-footed home the equaliser from just outside the six-yard box.
And with Arsenal coach Martin Palermo - a former Argentina international - pacing down the touchline demanding referee Andres Merlos to blow the whistle, Lautaro Acosta struck the winner in the 10th minute of added time.
Lanus launched one last foray forward and amid a host of bodies and a goal-mouth scramble, Acosta managed to poke the ball into the back of the net.
Earlier, Arsenal pair Brahian Aleman and Ramiro Carrera had given the 11th-placed visitors a 2-1 lead at half-time after cancelling out Silvio Romero's seventh-minute opener.
Guillermo Barros Schelotto's Lanus - unbeaten in 10 league games - are only two points adrift of River after 14 matches.
River remain unbeaten, though they were held to a 1-1 draw at Velez Sarsfield on Sunday.
Milton Caraglio headed eighth-placed Velez into an 18th-minute lead after rising highest inside the penalty area.
River, who booked a Copa Sudamericana semi-final showdown with bitter rivals Boca Juniors last week - hit back through Gabriel Mercado 20 minutes later.
Mercado fired a shot low and hard past Velez goalkeeper Sebastian Sosa.
Racing Club are three points off the pace thanks to a hard-fought 1-0 win at home to Banfield.
Gustavo Bou's seventh-minute goal was all that separated the two teams as Racing made it back-to-back wins and extended their undefeated run to five games in the league.
Emmanuel Gigliotti inspired Boca to a 2-0 win over Tigre.
Gigliotti scored twice in the second half as Boca moved level on points with fourth-placed Independiente, who suffered a 1-0 defeat at home to Gimnasia La Plata.
Leandro Fernandez's goal two minutes from time gave lowly Godoy Cruz a thrilling 4-3 victory against Atletico Rafaela.
Estudiantes were 1-0 winners over struggling Rosario Central, while Newell's Old Boys accounted for San Lorenzo 3-1.
Three second-half goals helped Belgrano to a 3-0 triumph against cellar-dwelling Defensa y Justicia, while Olimpo downed fellow strugglers Quilmes 2-1.
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