Henrique opened the scoring for the Brazilian giants in the 40th minute, but Carlos Lobaton equalised from the penalty spot eight minutes after the break.
Patrick Vieira netted the winner in the 22nd minute, firing a hard shot from inside the area into the left-upper corner of the net at Pacaembu Stadium, Sao Paulo.
Sporting Cristal are in Group Two with Palmeiras, Libertad of Paraguay and Tigre of Argentina.
Elsewhere, Newell's Old Boys of Argentina beat Paraguayan side Olimpia 3-1 in Group Seven and Chilean champions Huachipato shocked Gremio in Brazil as they won 2-1 to top Group Eight.
In Group Three, Bolivian side The Strongest saw off nine-man Arsenal of Argentina 2-1, FIFA.com reported.
The first week of the group stage closed with Tolima celebrating a 2-1 triumph over visitors Cerro Porteno of Paraguay in Colombia.