Boca, who began the weekend one point behind San Lorenzo and Tigre, took full advantage after the two teams lost 3-1 to Lanus and Estudiantes respectively.
Lucas Viatri put Boca ahead in the 36th minute when he tapped in an easy chance after Alvaro Gonzalez pulled the ball back from the byline.
Raul Saavedra equalised for promoted Tucuman with a long-range shot in the 59th minute but Boca regained the lead three minutes later when Luciano Figueroa volleyed in from Juan Roman Riquelme's free kick.
Boca had Jesus Datolo sent off for a second bookable offence in the 89th minute and San Martin's Facundo Perez followed in stoppage-time when he picked up a second yellow card for diving.
Former Manchester United and Lazio midfielder Juan Sebastian Veron gave Estudiantes an eighth-minute lead from a free kick against Tigre.
Veron also set up the second for Ivan Moreno y Fabianesi on the half hour before Leandro Benitez added a third in the 90th minute.
Carlos Luna headed one back in stoppage-time for Tigre.
With three matches to play, Boca lead with 32 points followed by San Lorenzo and Tigre on 30 and Lanus on 28.
Titleholders River Plate dropped back to the bottom after losing 2-1 at home to Argentinos Juniors. However, they are in no danger of relegation which is decided over three full seasons.
