Boselli converted a penalty in the sixth minute, scored again on the hour and tapped in from Enzo Perez's cross in the 71st. His tally is six goals in four matches in the Argentine league and the Libertadores Cup.
The Peruvian side's midfielder Roberto Guizasola was sent off on the stroke of half-time for a foul on Jose Sosa, on loan at Estudiantes from Bayern Munich.
Panamanian Luis Tejada equalised for Juan Aurich in the 34th when he beat Cristian Cellay to a low cross from the right to the near post where he steered the ball between keeper Agustin Orion's legs for his fourth goal in three matches in the competition.
Estudiantes, who had not conceded a goal at home in last year's campaign, were stung and Cellay made up for his mistake when he volleyed across the face of goal in the 43rd minute to allow fellow defender German Re to head in under the crossbar.
Substitute Leandro Gonzalez marked his Libertadores debut with the fifth two minutes from the end.
Cruzeiro, the Brazilian team who lost last year's final to Estudiantes, were beaten 2-0 away to 1994 champions Velez Sarsfield of Argentina after having two men sent off in the opening 37 minutes in Group Seven on Wednesday.
Brazil midfielder Gilberto was sent off after only two minutes for elbowing an opponent.
Uruguayan Santiago Silva, the Argentine Apertura championship's top scorer with Banfield in December with 14 goals, put Velez ahead three minutes later.
Substitute Juan Manuel Martinez added the second goal with a quarter of an hour to go.
Cruzeiro club president Zeze Perrela was quoted in Argentine media as calling Uruguayan referee Martin Vazquez a bandit and saying the competition's organisers wanted to see Velez go far in their centenary year.
