The top two sides had 100 per cent records from three games at the start of the day, and Lanus did at least remain unbeaten as they played out a goalless draw with Racing.
River, though, lost 2-0 at San Lorenzo, and the writing was on the wall early on.
Denis Stracqualursi opened the scoring in the first minute and Mauro Cetto doubled the advantage after 20 minutes.
The hosts had Gonzalo Veron sent off five minutes from time, but it was too late for River to take advantage.
Matias Perez Garcia scored twice as Tigre moved to within three points of the leaders with a 2-1 win over All Boys.
Perez Garcia opened the scoring from the spot after seven minutes and then, though the lead lasted just three minutes before Santiago Montoya equalised, added a second on the half-hour to clinch the points.
Matias Escobar of Tigre was dismissed in the 85th minute.
Goals from Damian Lizio (27), Bruno Bianchi (35) and Pablo Daniel Magnin (61) gave Union Santa Fe their first win of the campaign, 3-1 win over Boca Juniors, who pulled one back a minute from time through Santiago Silva.
In the day's other game, Argentinos Juniors survived late red cards from Lucas Rodriguez (73) and Anibal Matellan (85) to hold on for a goalless draw at Godoy Cruz.