A series of good results and performances under new coach Julio Cesar Falcioni in friendlies in January had led to Boca being named as the team to beat after some good signings and the return to the side of Juan Roman Riquelme.
Riquelme missed virtually all of the Apertura championship in the first half of the season following knee surgery last May.
Godoy Cruz, however, absorbed a lot of pressure in the first half and survived some good Boca chances including a shot from playmaker Riquelme that hit the base of the near post.
The visitors hit back on the break, two goals by striker Ruben Ramirez giving them a 2-0 half-time lead. Midfielder Adrian Torres added a third six minutes after the interval before new signing Walter Erviti pulled one back two minutes later.
Boca lost their shape chasing the match in the second half and speedy winger Carlos Sanchez, a thorn in the Boca defence, sealed the victory with a fine solo goal in stoppage time.
"When you lose you can't say it's bad luck, there was good work by our adversaries. We left spaces and they hurt us a lot," Falcioni told the post match news conference.
"We had four or five goal chances under the crossbar, we couldn't put them away, that's all... we deserved more, not to lose by this result.
"Whether or not we are (title) candidates, this defeat doesn't take anything away from us."
Boca's arch-rivals River Plate were held to a 0-0 draw at Tigre while Racing Club won 1-0 away to All Boys.
Title holders Estudiantes opened the championship with a 2-1 home victory over Newell's Old Boys and Velez Sarsfield, runners-up in the Apertura, came from two goals down for a 2-2 draw at Independiente on Friday.
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