Moreno, who previously played for Bolivia in the 1991, 1993, 1997 and 1999 Copa Americans, evened the score at 1-1 late in the first half when he dribbled through a maze of Venezuelan defenders and his shot deflected off a Venezuelan defender and rolled into the goal.
Venezuela went ahead a second time on a goal by Ricardo David Paez, son of Coach Richard Paez, but Bolivia rallied for the equalizer late in the game when Juan Carlos Arce scored with a shot to the near post.
In the other Group A opener, Peru shocked Uruguay, 3-0, on goals by Miguel Villalta, Juan Marino and Paolo Guerrero.
June 26 in Merida
Peru 3 Uruguay 0. Goals: Villalta 27, Marino 69, Guerrero 88.
Peru -- Butron, Galliquio, Villalta, Acasiete, Rodriguez, Vilchez, Pedro Garcia (Marino, 57), Bazalar, Farfan (De la Haza, 80), Pizarro (Mendoza, 77), Guerrero.
Uruguay -- Carini, Diogo, Lugano, Godin, D. Rodríguez, Diego Perez, Pablo Garcia, Canobbio (C.Rodriguez, 46), Estoyanoff (Vargas, 80), Forlan, Sanchez (Abreu, 66).
Referee: Carlos Amarilla (Paraguay).
June 26 in San Cristobal
Venezuela 2 Bolivia 2. Goals: Maldonado 20, Paez 55; Moreno 38, Arce 84.
Venezuela -- Vega, Gonzalez, Cichero, Rey, Rojas, Vera, Mea Vitali, Paez (Vielma, 72), Arango, Maldonado (Torrealba, 77), De Ornelas (Guerra, 59).
Bolivia -- Galarza, Hoyos, Raldes, J.M. Pena, Alvarez, Reyes (D.Pena, 59), Mojica, Vaca (Galindo, 70), Garcia, Moreno (Cabrera, 74), Arce.
Referee: Mauricio Reinoso (Ecuador).