Estudiantes, top of the standings on 36 points with two matches remaining, retained their one-point lead over Argentinos Juniors, 2-1 winners at San Lorenzo.
Independiente, who had led the standings throughout March, have virtually lost all chance of the title after a 3-2 home defeat by Boca Juniors left them five points behind.
Midfielder Omar Zarif put relegated Chacarita ahead in the 19th minute but striker Mauro Boselli equalised in the 32nd with a penalty, his 10th goal of the championship, after defender Lisandro Lopez had handled and was sent off.
Defender Christian Cellay headed the winner from a right cross before half time and there was a delay to the start of the second half while police attempted to wrest back a crowd-control hose from angry Chacarita fans.
Argentinos Juniors kept pace with the leaders when Ismael Sosa struck in the final minute with his second goal to give them a 2-1 away win over San Lorenzo.
PALERMO AGAIN
Boca, the country's most popular team who have fallen on difficult times, won away for the first time in 15 matches.
Independiente went ahead on the half hour through midfielder Ignacio Piatti but Boca hit back within two minutes when left-back Luciano Monzon drilled in a low shot from the edge of the box.
Talismanic striker Martin Palermo then scored another of his fluke goals in the 38th with help from Independiente keeper Adrian Gabbarini to take his record tally for the club to 222.
The goalkeeper came out poorly to a high ball on the edge of the six-yard box. Palermo, with his back to goal, rose above him to steer the ball tentatively with the back of head towards the net and it went in off the far post.
Substitute Pablo Mouche rifled in a fine third for Boca three minutes from time but was sent off for two yellow card offences in quick succession: taking off his shirt and provocative celebrations in front of home fans.
Striker Leonel Nunez pulled one back with a stoppage time penalty but the resigned look of Independiente coach Americo Gallego at the final whistle said volumes for how he felt about his team letting their title chances slip in the last few weeks.
