River dominated most of the match and striker David Trezeguet was just wide with two good chances but they were let down by poor defending at a set piece, a regular weakness in coach Matias Almeyda's team.
With 20 minutes remaining, Racing won a free kick on the right and left back Matias Cahais ghosted into the middle unmarked to head the ball into the net from close to the penalty spot.
Before the goal, Uruguayan substitute Rodrigo Mora headed River's best chance with goalkeeper Sebastian Saja making a superb diving save to deny the home side.
Racing, defensive from the start with no goal chances in the first half, owed their greater penetration in the second to the introduction of substitute Mauro Camoranesi in midfield.
The victory gave former Italy international Camoranesi his second win over friend and ex-Juventus team mate Trezeguet since the 2006 World Cup final in Berlin in which the former France striker was on the losing side after missing his penalty in the shootout.
RIOTING
No matter that the season does not end until June - relegation quickly becomes a serious issue for many teams due to the points averages in the league's convoluted system.
River, having just won promotion, are at a disadvantage and their total points this season must exceed the average points of most of the teams calculated over the last three seasons.
After two successive defeats and five matches without victory, River's average of 1.125 points from eight matches leaves them one from the bottom of the relegation table.
River, one of Argentina's 'Big Five' clubs with a record 33 league titles, were relegated for the first time in June 2011 when they lost a playoff against then-second division side Belgrano, prompting rioting from fans.
Rioters broke windows and doors at the Monumental, smashing parked cars and looting shops on nearby Libertador avenue, which looked like a war-zone two hours after the playoff ended.
Almeyda, a midfielder in the team that was relegated, steered them back into the top flight as second division champions in his first season as coach.
A string of good results would help them climb back out of trouble but the vast majority of the 40,000 crowd at the Monumental want Almeyda out, chanting the name of Ramon Diaz as their preferred choice.
Diaz steered River to five league titles between 1996 and 2002 but he and club president Daniel Passarella do not get on and Passarella publicly gave Almeyda his backing last week when media were casting doubt on the coach's future.
"We've got to press on, work is the only word that fits this situation. I have faith in my work and the squad. We'll pull through," Almeyda told reporters.
