The club have picked up only four points in the 'Inicial' championship, having been without Gutierrez for three games while waiting for the transfer papers to come through from his former team, Mexico's Cruz Azul.
It was the first home defeat in 42 matches as River coach for Ramon Diaz who returned at the end of last year for a third spell in charge, a decade after leaving in 2002.
The last time Diaz was beaten at home as River coach was in 1999.
The coach was satisfied with Sunday's first-half performance but River were hit twice on the break by strikers Facundo Curuchet and Ruben Ramirez in the second period before Gutierrez pulled a goal back three minutes from time.
Diaz was less pleased when River were denied a penalty in added time for handball by Colon defender Oscar Carniello, referee Fernando Rapallini deeming it unintentional.
"We don't want to be gifted anything but if it's handball then it should be punished," Diaz said.
It was an unhappy Sunday for Argentina's two biggest teams with River's arch-rivals Boca Juniors also losing 2-0 to Estudiantes in La Plata.
Boca have six points.
Argentinos Juniors and promoted Gimnasia-La Plata are equal top with nine points each. Gimnasia, who have a game in hand, play title holders Newell's Old Boys in Rosario on Tuesday.
- Sports & Recreation
- Ramon Diaz