Gelmin Rivas scored his fifth goal of the season to give Tachira a 33rd-minute lead with Jose Reyes doubling the away side's advantage midway through the second half.
An 88th-minute goal from Alan Sierra gave Zulia hope but the league leaders were able to hold on to ensure they remained at the summit of the Apertura table.
Tucanes collected their third consecutive win to remain two points behind Tachira after they defeated Portuguesa 2-0.
After a scoreless first half, Jose Parada put the home side ahead with 13 minutes to play before Gilson Salazar made the game safe with a goal deep into injury time.
Three goals in the final 15 minutes saw Deportivo La Guaira run away with a 3-0 win over Metropolitanos.
An uneventful first half gave way to a flurry of activity in the second, with Framber Villegas putting the home side ahead in the 76th minute.
Javier Garcia scored his second goal of the campaign to give Deportivo La Guarira a two-goal cushion, before Luciano Ursino rounded out the victory in injury time.
The result leaves Metropolitanos languishing in 17th place on the table, while Deportivo remain one game off top.
Deportivo Anzoategui were at their destructive best as they crushed Llaneros De Guanare 5-0 at home.
Edwin Aguilar scored within the opening 10 minutes to send Ruberth Moran's side on their way, with goals from William Diaz and Evelio Hernandez building a commanding advantage before half-time.
Llaneros had no answers in the second period as their opponents scored two more goals through Manuel Arteaga and Ricardo Martins to complete the rout.
Carabobo escaped with a point against Atletico Venezuela after Daniel Mustafa turned the ball into his own net seven minutes from time, cancelling out Leonardo Carboni's 65th-minute strike as the match ended in a 1-1 draw.
Estudiantes de Merida and Deportivo Petare could not be seperated in their clash as they also drew 1-1, with Zamora and Mineros de Guayana also in a 1-1 stalemate.
Neither Deportivo Lara or Trujillanos could find the back of the net in their 0-0 draw as both sides remain in the bottom half of the table with four points each.