Clemente Rodriguez's goal after 17 minutes was all that separated the two sides, while Estudiantes finished the match with 10 men following the last-minute dismissal of Matias Sanchez.
The win gives Boca breathing space over nearest challengers Racing Club.
Tigre climbed to fifth with a 1-0 win at Argentinos Juniors, courtesy of a Carlos Luna goal 10 minutes into the second half.
Pablo Barzola was sent off for Argentinos 19 minutes from time.
A late goal from Armando Cooper earned Godoy Cruz a 1-1 draw against Union Santa Fe.
The visitors led through a 63rd-minute goal from Rodrigo Erramuspe until Cooper's equaliser seven minutes from time.