River, who finished bottom of the Apertura championship last year and were playing their first competitive game under new coach Nestor Gorosito, appeared to be heading for a handsome win as they went 2-0 ahead after the break.
Gustavo Cabral headed the first in the 57th minute and Colombian Radamel Garcia Falcao turned in Mauro Rosales's pass to double their lead 12 minutes later.
But Colon pulled one back out of the blue when Alejandro Capurro scored with a swerving 30-metre shot in the 77th minute before substitute Pablo Calandria equalised with another long-range shot in the second minute of injury-time.
Colon played the entire second half with 10 men after Pablo Aguilar was sent off in the 44th minute for hacking down an opponent.
Defending champions Boca Juniors began with a fortuitous 2-1 win at Gimnasia-Jujuy.
Ricardo Noir put Boca ahead in the 73rd minute, scoring from a rebound after Gaston Pezzutti failed to hold Nicolas Gaitan's shot, and Lucas Viatri scored a second from Juan Roman Riquelme's back-heeled pass 11 minutes later.
Pablo Calandria pulled one back for the hosts to give Boca an uncomfortable final few minutes.
