River have been playing poorly since winning the Clausura more than a year ago and were beaten 2-0 at Banfield at the start of the season last week.
The first half ended level at 2-2 after their solitary striker Matias Alustiza twice equalised, his second a penalty on the stroke of halftime.
Chacarita went ahead in the 53rd minute through midfielder Facundo Parra, which was when under-fire coach Nestor Gorosito's reliance on River's old guard of Ortega, Marcelo Gallardo and Matias Almeyda paid off.
Ortega laid on River's equaliser for substitute striker Daniel Villalba in the 68th and lobbed an exquisite winner with three minutes remaining.
Boca Juniors, held 2-2 at home by Argentinos Juniors last week, won 2-1 away to Lanus, again without playmaker Juan Roman Riquelme, who was suspended for the first match and nursing a knee problem on Sunday.
Striker Martin Palermo, the focus of criticism from Boca fans in midweek over an alleged desire to play for his former club Estudiantes in the Club World Cup in December, scored the winner.
VERON INJURED
South American champions Estudiantes beat city rivals Gimnasia 3-0 in the La Plata derby with captain Juan Sebastian Veron suffering a pulled muscle that makes him doubtful for Argentina's key World Cup qualifier against Brazil next Saturday.
Teenage midfielder Patricio Rodriguez scored his first two goals in the first division as Independiente came from behind to beat promoted nine-man Atletico Tucuman 4-2.
Atletico went ahead in the 21st minute when Cesar Montiglio scored but the defender was sent off three minutes later.
They held the lead until striker Dario Gandin equalised in the 64th, netting the rebound after his penalty was parried by keeper Lucas Ischuk, and Rodriguez put Independiente ahead three minutes later.
The home side had Paraguayan midfielder Fabio Escobar sent off in the 80th minute but still managed to equalise one minute later through striker Luis Rodriguez.
However, with two extra men, Independiente scored twice in the last six minutes - a drive from outside the box by Rodriguez and a stoppage-time fourth goal by substitute Leonel Nunez.
Champions Velez Sarsfield beat Arsenal 3-1 and are second behind leaders Estudiantes on goal difference with six points from two matches.
Newell's Old Boys and Rosario Central also have six points.
