Copa Libertadores Roundup, Feb 19
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Sosa scored after eight seconds for Estudiantes, but a hat trick from Wilmer Aguirre and a fourth from Jose Fernandez gave Alianza victory and top spot in Group 3.
In the day's other match, Juan Manuel Olivera scored a 3rd minute penalty to give Universidad de Chile a 1-0 home win over Venezuela's Caracas in the opening Group 8 match.
In Lima, Sosa charged down an attempted clearance direct from kick off and rounded goalkeeper Salomon Libman to score opener for Estudiantes.
Aguirre cut into the box and fired into the roof of the net for Alianza's equalizer in the 18th minute, then muscled his way past two defenders to score his second in the 34th.
Aguirre completed his treble in the 74th and Fernandez sealed the win in the 83rd.
Alianza leads the group with two wins from two games.
Juan Manuel Olivera scored the only goal of the match at Santiago after he was fouled in the box by Juan Manuel Rey.
Flamengo of Brazil hosts Universidad Catolica of Chile in Group 8 next Wednesday.
The Copa Libertadores is the top club competition in Latin America. Eight group winners plus the six best placed runners-up qualify for the last 16.
Mexican clubs San Luis and Guadalajara will enter at the last 16 stage after pulling out of last year's tournament at the same stage because of the swine flu outbreak.